TI83-84 Reference

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Unformatted text preview: Triola_GraphRefCard 11/13/07 3:48 PM Page 1 TI-83/TI-84 Plus Reference T HE T RIOLA S TATISTICS S ERIES SORTING A LIST OF DATA To sort (arrange in order) a list of data, press K, then use the arrow keys to select SortA( if an ascending order is desired, or select SortD( if a descending order is desired. Press [, then enter the list name. Example: To sort the data in list L1 in ascending order, enter SortA(L1) and press [. NAMING A LIST OF DATA Lists L1, L2, L3, L4, L5, L6 are likely to be used often, but they do not have meaningful names. To store a list with a meaningful name, save the list with a name by using the Y key. Example: To store the data in L1 as a list with the name of AGE, enter L1 : AGE by pressing the sequence of keys indicated here: 2. Calculator Initial Setup and B asic Operation MODE SETTINGS Turn the calculator on by pressing the Z key. Press G to access these settings: To change any setting to those shown here, use the arrow keys e f g h to highlight the correct option, then press [ to make the change. Press P when done. Select STAT PLOTS by pressing F E. Verify that only the first plot is in the On state, as shown below. If any other plot is On, change it to Off by scrolling to it, pressing [, then scrolling to the right to highlight Off. Then press [ and select QUIT by pressing F G. Scatterplot A scatterplot requires paired data, so enter the data in two lists, such as L1 and L2. Named lists can also be used. 1. Enter the paired data in two lists, such as L1 and L2. Also, perform the initial setup described under the heading of Graphs: Initial Setup. 2. Select the STAT PLOTS menu by pressing F E. 3. Press [. 4. Be sure that the Plot1 screen is On. Use the arrow keys to select the type of graph. The screen at the right shows the generic scatterplot highlighted, as it should be. 5. For the Xlist entry, enter the label or name of the list containing the data to be used for the x variable. For the Ylist entry, enter the label or name of the list containing the data to be used for the y variable. The above screen shows that the scatterplot will be graphed using the data in lists L1 and L2. 6. For the bottom item of Mark, select the character to be used for plotting the points in the scatterplot. 7. Press B 9 to select ZoomStat, which allows the calculator to automatically select settings that allow the graph to fit the screen. (To use your own settings, press A, enter your own settings, then press D.) Shown here is a typical scatterplot. By pressing C and using the arrow keys, coordinates of individual points can be identified. Boxplot 1. To obtain a boxplot from a single list of values, enter the data values and store them as a list, such as L1 or a named list, such as AGE. Also, perform the initial setup described under the heading of Graphs: Initial Setup. Select the STAT PLOTS menu by pressing F E. Press [. Be sure that the Plot1 screen is On. Use the arrow keys to select the boxplot as shown in the screen below. 2. 3. 4. L1 F enables function above another key. I enables alphabet character above another key. : Y A IL G IT E I 0. F1 Use arrow keys e f g h to move cursor. P clears entry and answers. c Minus sign for operation of subtraction. The list of data named AGE will be stored until it is removed. To retrieve a named list of data, access the LIST menu by pressing F K, then use the down arrow key e to scroll to the desired list, then press [ [. The data will be displayed in one or more rows enclosed within a set of braces. The named list can be used with other functions, such as the construction of a confidence interval or a hypothesis test. Histogram 1. Enter the data values and store them as a list, such as L1 or a named list, such as AGE. Also, perform the initial setup described in the preceding two steps. Select the STAT PLOTS menu by pressing F E. The screen should appear as shown in step 2 above. Press [. Be sure that the Plot1 screen is On. Use the arrow keys to select the type of graph. The screen below shows the histogram highlighted, as it should be. SCREEN BRIGHTNESS Increase darkness of the display by pressing F, then pressing and holding the up arrow key h . Decrease darkness of the display by pressing F, then pressing and holding e. RETRIEVING A NAMED LIST OF DATA 5. TURN OFF CALCULATOR Turn the calculator off by pressing F, then Z. CLEAR SCREEN Press P to clear the screen. If an entry is required and P doesn’t work, select the QUIT option by pressing F G. ACCESSING FUNCTIONS ABOVE KEYS The F key enables the function or character with the same color printed above other keys. Example: The distribution menu is identified by DISTR printed above the O key in the same color as the F key, so access the DISTR menu by pressing F O. 2. 3. 4. Z turns calculator on. : Negative sign [ evaluates entry or executes an instruction or selects menu item. ACCESSING ALPHA CHARACTERS ABOVE KEYS The I key enables the alphabet characters printed above other keys. Example: Press I 1 to display the character Y. MATH OPERATIONS Use a b c d for addition, multiplication, subtraction, division. Press [ to evaluate. Example: To clear lists L1 and L2, select the ClrList menu item and then press F 1 , F 2. Press [ to execute. ENTER AND STORE DATA IN A LIST To enter and store data in any of the six lists L1, L2, L3, L4, L5, L6, press K, then select the default menu item of EDIT by pressing [. Use the arrow keys to move the cursor to the desired list. Enter a value and press [, enter another value and press [, and so on, until all data values have been entered. To exit the list screen, select QUIT by pressing F G. Example: To enter the values 5, 8, 16 in list L1, the screen should appear as shown below. DELETING A NAMED LIST Hint: Depending on the calculator model, storing too much data can create memory problems, so it is wise to delete any lists that are obsolete. Follow these steps to delete a named list from memory. 1. Access the MEM (memory) menu by pressing F a. 2. Use the down arrow key to scroll to 2:Mem Mgmt/Del, then press [. 3. Scroll to 4:List as shown in the screen at the right. 4. Press [. 5. Scroll to the name of the list to be deleted. 6. Press H and the named list will be deleted from memory. 6. 7. For the Xlist entry, enter the label or name of the list containing the data to be graphed. The above screen shows that the boxplot will be graphed using the data in list L1. By selecting the generic boxplot in the middle of the second row of the graph types, you are selecting the basic boxplot described in the textbook. If you select the other boxplot, the result will be a modified boxplot, which shows outliers. For the Freq (frequency) entry, enter 1 so that each value is used once. Press B 9 to select ZoomStat, which allows the calculator to automatically select settings that allow the graph to fit the screen. 5. 6. 7. Example: To evaluate 5 * 4, press 5 b 4 [ to get the result of 20. Use c for subtraction, as in 8 - 3. Use : for negative sign, as in -5. Apps (Applications) Textbooks in the Triola statistics series typically come with a CDROM that includes an app consisting of the lists of data found in Appendix B. An app can be downloaded to the calculator, so that the lists of data sets are available for the entire course. (The TI-83 does not allow the use of apps.) Download instructions can be obtained from the Texas Instruments Web site. Refer to Appendix B in the textbook for the names of the individual lists. For the Xlist entry, enter the label or name of the list containing the data to be graphed. The above screen shows that the histogram will be graphed using the data in list L1. For the Freq (frequency) entry, enter 1 so that each value is used once. Press B 9 to select ZoomStat, which allows the calculator to determine the class width and boundaries. To obtain boxplots for two or three lists of data, follow the above steps, but turn on Plot2 and/or Plot3. Use Plot2 and/or Plot3 to set up boxplots for the additional data sets. Shown below is a screen showing a single boxplot, along with another screen showing two boxplots. Whether using one, two, or three boxplots, press C and use the arrow keys to see values of the minimum, maximum, and quartiles. Frequency Polygon 1. First, manually construct a frequency distribution as a table with class midpoint values listed in the first column and the corresponding class frequencies listed in the second column. Enter the class midpoint values in list L1. Enter the class frequencies in list L2. Select the STAT PLOTS menu by pressing F E. Press [. Make the selections shown in the screen below. NOTE Use U for an exponent. Example: To evaluate 23, press 2 U 3 [ to obtain the result of 8. POWER/EXPONENT Shown below is a typical histogram. By pressing C and using the arrow keys, heights of the bars can be identified. The second display shows that the third class has frequency n = 23 and includes values greater than or equal to 26.877834 (indicated by min = 26.877834) and less than 31.94831 (indicated by max 6 31.94831). To use your own class width and boundaries, press A and make your own entries (where Xscl is the bar width), then press D. 2. 3. 4. 5. 6. The screen shown below is an example of a modified boxplot. The points at the right are outliers. Lists of Data CLEARING AND ENTERING LISTS L1, L2, L3, L4, L5, L6 can be used to enter and store lists of data. Hint: Clear lists before entering data. more➤ Graphs: Initial Setup Many graphing difficulties can be avoided by performing an initial setup consisting of these two steps: 1. Press the E key, and then press P to delete any existing expressions, so that the screen appears as shown below. Then select QUIT by pressing F G. CLEAR LISTS Press K to get the menu in the screen shown here. Press e to scroll down and select 4:ClrList, then press [. The screen should display ClrList. Enter the lists to be cleared, separated by commas. more➤ HINT Comparisons of two or three data sets are made easier if the boxplots are graphed in the same window. 7. Press B 9 to select ZoomStat, which allows the calculator to automatically use settings that allow the graph to fit the screen. ,!7IA3C1-djjgha!:t;K;k;K;k ISBN 0-321-39967-6 1 more➤ 2 3 Triola_GraphRefCard 3/29/06 3:26 PM Page 1 T H E T R I O L A S TAT I S T I C S S E R I E S TI-83/TI-84 Plus Reference A DDISON -W ESLEY Created in conjunction with Calculator Initial Setup and B asic Operation MODE SETTINGS Turn the calculator on by pressing the Z key. Press G to access these settings: To change any setting to those shown here, use the arrow keys e f g h to highlight the correct option, then press [ to make the change. Press P when done. Increase darkness of the display by pressing F, then pressing and holding the up arrow key h . Decrease darkness of the display by pressing F, then pressing and holding e. SORTING A LIST OF DATA To sort (arrange in order) a list of data, press K, then use the arrow keys to select SortA( if an ascending order is desired, or select SortD( if a descending order is desired. Press [, then enter the list name. Example: To sort the data in list L1 in ascending order, enter SortA(L1) and press [. NAMING A LIST OF DATA Lists L1, L2, L3, L4, L5, L6 are likely to be used often, but they do not have meaningful names. To store a list with a meaningful name, save the list with a name by using the Y key. Example: To store the data in L1 as a list with the name of AGE, enter L1 : AGE by pressing the sequence of keys indicated here: 2. Select STAT PLOTS by pressing F E. Verify that only the first plot is in the On state, as shown below. If any other plot is On, change it to Off by scrolling to it, pressing [, then scrolling to the right to highlight Off. Then press [ and select QUIT by pressing F G. Scatterplot A scatterplot requires paired data, so enter the data in two lists, such as L1 and L2. Named lists can also be used. 1. Enter the paired data in two lists, such as L1 and L2. Also, perform the initial setup described under the heading of Graphs: Initial Setup. 2. Select the STAT PLOTS menu by pressing F E. 3. Press [. 4. Be sure that the Plot1 screen is On. Use the arrow keys to select the type of graph. The screen at the right shows the generic scatterplot highlighted, as it should be. 5. For the Xlist entry, enter the label or name of the list containing the data to be used for the x variable. For the Ylist entry, enter the label or name of the list containing the data to be used for the y variable. The above screen shows that the scatterplot will be graphed using the data in lists L1 and L2. 6. For the bottom item of Mark, select the character to be used for plotting the points in the scatterplot. 7. Press B 9 to select ZoomStat, which allows the calculator to automatically select settings that allow the graph to fit the screen. (To use your own settings, press A, enter your own settings, then press D.) Shown here is a typical scatterplot. By pressing C and using the arrow keys, coordinates of individual points can be identified. Boxplot 1. To obtain a boxplot from a single list of values, enter the data values and store them as a list, such as L1 or a named list, such as AGE. Also, perform the initial setup described under the heading of Graphs: Initial Setup. Select the STAT PLOTS menu by pressing F E. Press [. Be sure that the Plot1 screen is On. Use the arrow keys to select the boxplot as shown in the screen below. 2. 3. 4. L1 F enables function above another key. I enables alphabet character above another key. : Y A IL G IT E I 0. F1 Use arrow keys e f g h to move cursor. P clears entry and answers. c Minus sign for operation of subtraction. The list of data named AGE will be stored until it is removed. Histogram 1. Enter the data values and store them as a list, such as L1 or a named list, such as AGE. Also, perform the initial setup described in the preceding two steps. Select the STAT PLOTS menu by pressing F E. The screen should appear as shown in step 2 above. Press [. Be sure that the Plot1 screen is On. Use the arrow keys to select the type of graph. The screen below shows the histogram highlighted, as it should be. SCREEN BRIGHTNESS RETRIEVING A NAMED LIST OF DATA TURN OFF CALCULATOR Turn the calculator off by pressing F, then Z. CLEAR SCREEN Press P to clear the screen. If an entry is required and P doesn’t work, select the QUIT option by pressing F G. ACCESSING FUNCTIONS ABOVE KEYS The F key enables the function or character with the same color printed above other keys. Example: The distribution menu is identified by DISTR printed above the O key in the same color as the F key, so access the DISTR menu by pressing F O. To retrieve a named list of data, access the LIST menu by pressing F K, then use the down arrow key e to scroll to the desired list, then press [ [. The data will be displayed in one or more rows enclosed within a set of braces. The named list can be used with other functions, such as the construction of a confidence interval or a hypothesis test. 5. 2. 3. 4. Z turns calculator on. : Negative sign [ evaluates entry or executes an instruction or selects menu item. ACCESSING ALPHA CHARACTERS ABOVE KEYS The I key enables the alphabet characters printed above other keys. Example: Press I 1 to display the character Y. MATH OPERATIONS Use a b c d for addition, multiplication, subtraction, division. Press [ to evaluate. Example: To evaluate 5 * 4, press 5 b 4 [ to get the result of 20. Use c for subtraction, as in 8 - 3. Use : for negative sign, as in -5. Example: To clear lists L1 and L2, select the ClrList menu item and then press F 1 , F 2. Press [ to execute. ENTER AND STORE DATA IN A LIST To enter and store data in any of the six lists L1, L2, L3, L4, L5, L6, press K, then select the default menu item of EDIT by pressing [. Use the arrow keys to move the cursor to the desired list. Enter a value and press [, enter another value and press [, and so on, until all data values have been entered. To exit the list screen, select QUIT by pressing F G. Example: To enter the values 5, 8, 16 in list L1, the screen should appear as shown below. DELETING A NAMED LIST Hint: Depending on the calculator model, storing too much data can create memory problems, so it is wise to delete any lists that are obsolete. Follow these steps to delete a named list from memory. 1. Access the MEM (memory) menu by pressing F a. 2. Use the down arrow key to scroll to 2:Mem Mgmt/Del, then press [. 3. Scroll to 4:List as shown in the screen at the right. 4. Press [. 5. Scroll to the name of the list to be deleted. 6. Press H and the named list will be deleted from memory. 6. 7. For the Xlist entry, enter the label or name of the list containing the data to be graphed. The above screen shows that the boxplot will be graphed using the data in list L1. By selecting the generic boxplot in the middle of the second row of the graph types, you are selecting the basic boxplot described in the textbook. If you select the other boxplot, the result will be a modified boxplot, which shows outliers. For the Freq (frequency) entry, enter 1 so that each value is used once. Press B 9 to select ZoomStat, which allows the calculator to automatically select settings that allow the graph to fit the screen. 5. 6. 7. Apps (Applications) Textbooks in the Triola statistics series typically come with a CDROM that includes an app consisting of the lists of data found in Appendix B. An app can be downloaded to the calculator, so that the lists of data sets are available for the entire course. (The TI-83 does not allow the use of apps.) Download instructions can be obtained from the Texas Instruments Web site. Refer to Appendix B in the textbook for the names of the individual lists. For the Xlist entry, enter the label or name of the list containing the data to be graphed. The above screen shows that the histogram will be graphed using the data in list L1. For the Freq (frequency) entry, enter 1 so that each value is used once. Press B 9 to select ZoomStat, which allows the calculator to determine the class width and boundaries. To obtain boxplots for two or three lists of data, follow the above steps, but turn on Plot2 and/or Plot3. Use Plot2 and/or Plot3 to set up boxplots for the additional data sets. Shown below is a screen showing a single boxplot, along with another screen showing two boxplots. Whether using one, two, or three boxplots, press C and use the arrow keys to see values of the minimum, maximum, and quartiles. Frequency Polygon 1. First, manually construct a frequency distribution as a table with class midpoint values listed in the first column and the corresponding class frequencies listed in the second column. Enter the class midpoint values in list L1. Enter the class frequencies in list L2. Select the STAT PLOTS menu by pressing F E. Press [. Make the selections shown in the screen below. NOTE POWER/EXPONENT Use U for an exponent. Example: To evaluate 23, press 2 U 3 [ to obtain the result of 8. Shown below is a typical histogram. By pressing C and using the arrow keys, heights of the bars can be identified. The second display shows that the third class has frequency n = 23 and includes values greater than or equal to 26.877834 (indicated by min = 26.877834) and less than 31.94831 (indicated by max 6 31.94831). To use your own class width and boundaries, press A and make your own entries (where Xscl is the bar width), then press D. 2. 3. 4. 5. 6. The screen shown below is an example of a modified boxplot. The points at the right are outliers. Lists of Data CLEARING AND ENTERING LISTS L1, L2, L3, L4, L5, L6 can be used to enter and store lists of data. Hint: Clear lists before entering data. more➤ Graphs: Initial Setup Many graphing difficulties can be avoided by performing an initial setup consisting of these two steps: 1. Press the E key, and then press P to delete any existing expressions, so that the screen appears as shown below. Then select QUIT by pressing F G. HINT CLEAR LISTS Press K to get the menu in the screen shown here. Press e to scroll down and select 4:ClrList, then press [. The screen should display ClrList. Enter the lists to be cleared, separated by commas. more➤ Comparisons of two or three data sets are made easier if the boxplots are graphed in the same window. ,!7IA3C1-djjgha!:t;K;k;K;k ISBN 0-321-39967-6 1 7. Press B 9 to select ZoomStat, which allows the calculator to automatically use settings that allow the graph to fit the screen. more➤ 2 3 Triola_GraphRefCard 3/29/06 3:26 PM Page 1 T H E T R I O L A S TAT I S T I C S S E R I E S TI-83/TI-84 Plus Reference A DDISON -W ESLEY Created in conjunction with Calculator Initial Setup and B asic Operation MODE SETTINGS Turn the calculator on by pressing the Z key. Press G to access these settings: To change any setting to those shown here, use the arrow keys e f g h to highlight the correct option, then press [ to make the change. Press P when done. Increase darkness of the display by pressing F, then pressing and holding the up arrow key h . Decrease darkness of the display by pressing F, then pressing and holding e. SORTING A LIST OF DATA To sort (arrange in order) a list of data, press K, then use the arrow keys to select SortA( if an ascending order is desired, or select SortD( if a descending order is desired. Press [, then enter the list name. Example: To sort the data in list L1 in ascending order, enter SortA(L1) and press [. NAMING A LIST OF DATA Lists L1, L2, L3, L4, L5, L6 are likely to be used often, but they do not have meaningful names. To store a list with a meaningful name, save the list with a name by using the Y key. Example: To store the data in L1 as a list with the name of AGE, enter L1 : AGE by pressing the sequence of keys indicated here: 2. Select STAT PLOTS by pressing F E. Verify that only the first plot is in the On state, as shown below. If any other plot is On, change it to Off by scrolling to it, pressing [, then scrolling to the right to highlight Off. Then press [ and select QUIT by pressing F G. Scatterplot A scatterplot requires paired data, so enter the data in two lists, such as L1 and L2. Named lists can also be used. 1. Enter the paired data in two lists, such as L1 and L2. Also, perform the initial setup described under the heading of Graphs: Initial Setup. 2. Select the STAT PLOTS menu by pressing F E. 3. Press [. 4. Be sure that the Plot1 screen is On. Use the arrow keys to select the type of graph. The screen at the right shows the generic scatterplot highlighted, as it should be. 5. For the Xlist entry, enter the label or name of the list containing the data to be used for the x variable. For the Ylist entry, enter the label or name of the list containing the data to be used for the y variable. The above screen shows that the scatterplot will be graphed using the data in lists L1 and L2. 6. For the bottom item of Mark, select the character to be used for plotting the points in the scatterplot. 7. Press B 9 to select ZoomStat, which allows the calculator to automatically select settings that allow the graph to fit the screen. (To use your own settings, press A, enter your own settings, then press D.) Shown here is a typical scatterplot. By pressing C and using the arrow keys, coordinates of individual points can be identified. Boxplot 1. To obtain a boxplot from a single list of values, enter the data values and store them as a list, such as L1 or a named list, such as AGE. Also, perform the initial setup described under the heading of Graphs: Initial Setup. Select the STAT PLOTS menu by pressing F E. Press [. Be sure that the Plot1 screen is On. Use the arrow keys to select the boxplot as shown in the screen below. 2. 3. 4. L1 F enables function above another key. I enables alphabet character above another key. : Y A IL G IT E I 0. F1 Use arrow keys e f g h to move cursor. P clears entry and answers. c Minus sign for operation of subtraction. The list of data named AGE will be stored until it is removed. Histogram 1. Enter the data values and store them as a list, such as L1 or a named list, such as AGE. Also, perform the initial setup described in the preceding two steps. Select the STAT PLOTS menu by pressing F E. The screen should appear as shown in step 2 above. Press [. Be sure that the Plot1 screen is On. Use the arrow keys to select the type of graph. The screen below shows the histogram highlighted, as it should be. SCREEN BRIGHTNESS RETRIEVING A NAMED LIST OF DATA TURN OFF CALCULATOR Turn the calculator off by pressing F, then Z. CLEAR SCREEN Press P to clear the screen. If an entry is required and P doesn’t work, select the QUIT option by pressing F G. ACCESSING FUNCTIONS ABOVE KEYS The F key enables the function or character with the same color printed above other keys. Example: The distribution menu is identified by DISTR printed above the O key in the same color as the F key, so access the DISTR menu by pressing F O. To retrieve a named list of data, access the LIST menu by pressing F K, then use the down arrow key e to scroll to the desired list, then press [ [. The data will be displayed in one or more rows enclosed within a set of braces. The named list can be used with other functions, such as the construction of a confidence interval or a hypothesis test. 5. 2. 3. 4. Z turns calculator on. : Negative sign [ evaluates entry or executes an instruction or selects menu item. ACCESSING ALPHA CHARACTERS ABOVE KEYS The I key enables the alphabet characters printed above other keys. Example: Press I 1 to display the character Y. MATH OPERATIONS Use a b c d for addition, multiplication, subtraction, division. Press [ to evaluate. Example: To evaluate 5 * 4, press 5 b 4 [ to get the result of 20. Use c for subtraction, as in 8 - 3. Use : for negative sign, as in -5. Example: To clear lists L1 and L2, select the ClrList menu item and then press F 1 , F 2. Press [ to execute. ENTER AND STORE DATA IN A LIST To enter and store data in any of the six lists L1, L2, L3, L4, L5, L6, press K, then select the default menu item of EDIT by pressing [. Use the arrow keys to move the cursor to the desired list. Enter a value and press [, enter another value and press [, and so on, until all data values have been entered. To exit the list screen, select QUIT by pressing F G. Example: To enter the values 5, 8, 16 in list L1, the screen should appear as shown below. DELETING A NAMED LIST Hint: Depending on the calculator model, storing too much data can create memory problems, so it is wise to delete any lists that are obsolete. Follow these steps to delete a named list from memory. 1. Access the MEM (memory) menu by pressing F a. 2. Use the down arrow key to scroll to 2:Mem Mgmt/Del, then press [. 3. Scroll to 4:List as shown in the screen at the right. 4. Press [. 5. Scroll to the name of the list to be deleted. 6. Press H and the named list will be deleted from memory. 6. 7. For the Xlist entry, enter the label or name of the list containing the data to be graphed. The above screen shows that the boxplot will be graphed using the data in list L1. By selecting the generic boxplot in the middle of the second row of the graph types, you are selecting the basic boxplot described in the textbook. If you select the other boxplot, the result will be a modified boxplot, which shows outliers. For the Freq (frequency) entry, enter 1 so that each value is used once. Press B 9 to select ZoomStat, which allows the calculator to automatically select settings that allow the graph to fit the screen. 5. 6. 7. Apps (Applications) Textbooks in the Triola statistics series typically come with a CDROM that includes an app consisting of the lists of data found in Appendix B. An app can be downloaded to the calculator, so that the lists of data sets are available for the entire course. (The TI-83 does not allow the use of apps.) Download instructions can be obtained from the Texas Instruments Web site. Refer to Appendix B in the textbook for the names of the individual lists. For the Xlist entry, enter the label or name of the list containing the data to be graphed. The above screen shows that the histogram will be graphed using the data in list L1. For the Freq (frequency) entry, enter 1 so that each value is used once. Press B 9 to select ZoomStat, which allows the calculator to determine the class width and boundaries. To obtain boxplots for two or three lists of data, follow the above steps, but turn on Plot2 and/or Plot3. Use Plot2 and/or Plot3 to set up boxplots for the additional data sets. Shown below is a screen showing a single boxplot, along with another screen showing two boxplots. Whether using one, two, or three boxplots, press C and use the arrow keys to see values of the minimum, maximum, and quartiles. Frequency Polygon 1. First, manually construct a frequency distribution as a table with class midpoint values listed in the first column and the corresponding class frequencies listed in the second column. Enter the class midpoint values in list L1. Enter the class frequencies in list L2. Select the STAT PLOTS menu by pressing F E. Press [. Make the selections shown in the screen below. NOTE POWER/EXPONENT Use U for an exponent. Example: To evaluate 23, press 2 U 3 [ to obtain the result of 8. Shown below is a typical histogram. By pressing C and using the arrow keys, heights of the bars can be identified. The second display shows that the third class has frequency n = 23 and includes values greater than or equal to 26.877834 (indicated by min = 26.877834) and less than 31.94831 (indicated by max 6 31.94831). To use your own class width and boundaries, press A and make your own entries (where Xscl is the bar width), then press D. 2. 3. 4. 5. 6. The screen shown below is an example of a modified boxplot. The points at the right are outliers. Lists of Data CLEARING AND ENTERING LISTS L1, L2, L3, L4, L5, L6 can be used to enter and store lists of data. Hint: Clear lists before entering data. more➤ Graphs: Initial Setup Many graphing difficulties can be avoided by performing an initial setup consisting of these two steps: 1. Press the E key, and then press P to delete any existing expressions, so that the screen appears as shown below. Then select QUIT by pressing F G. HINT CLEAR LISTS Press K to get the menu in the screen shown here. Press e to scroll down and select 4:ClrList, then press [. The screen should display ClrList. Enter the lists to be cleared, separated by commas. more➤ Comparisons of two or three data sets are made easier if the boxplots are graphed in the same window. ,!7IA3C1-djjgha!:t;K;k;K;k ISBN 0-321-39967-6 1 7. Press B 9 to select ZoomStat, which allows the calculator to automatically use settings that allow the graph to fit the screen. more➤ 2 3 Triola_GraphRefCard 3/29/06 3:26 PM Page 2 T H E T R I O L A S TAT I S T I C S S E R I E S Descriptive Statistics FROM A LIST OF DATA Use the following procedure to find statistics including the mean, standard deviation, and the fivenumber summary. 1. Enter the data in a list, such as L1. A named list, such as AGE, can also be used. 2. Press K. 3. Use the right or left arrow keys to select the menu item of CALC, as shown in the screen below. TI-83/TI-84 Plus Reference Binomial Distribution 1. 2. Press F O for the DISTR (distribution) menu. The DISTR menu includes these two items: binompdf( Gives binomial probabilities for individual values of x. binomcdf( Gives cumulative probabilities (sum of the probabilities for values from 0 up to and including a desired value of x). Select one of the items from step 2. Both items require an entry of n, p, and an optional entry of x. Examples based on n = 8 and p = 0.4: binompdf(8, 0.4, 3) Provides probability for x = 3 binompdf(8, 0.4) Provides the nine probabilities for x = 0 through x = 8 Student t Distribution FINDING AREA 1. 2. 3. Press F O for the DISTR (distribution) menu. Select tcdf, which is used with this format: tcdf(lower bound, upper bound, df) Press [ and the area will be displayed. Confidence Intervals 1. 2. Press K, then use the arrow keys to select TESTS. Use the arrow keys to scroll to the appropriate confidence interval, then press [. Hypothesis Tests: Proportions and Means 1. 2. Press K, then use the arrow keys to select TESTS. Use the arrow keys to choose the correct test. One proportion: 1-PropZTest Two proportions: 2-PropZTest One mean: Z-Test or T-Test (Use T-Test if s is not known.) Two means: 2-SampZTest or 2-SampTTest (Use 2-SampTTest if s1 and s2 are not known.) Press [. 6. 7. For b & r select the option of Z 0 (for a null hypothesis of H0: r = 0). Scroll down to Calculate and press [. Results include intercept (a) and slope (b) of regression equation and linear correlation coefficient r. Results do not all fit on one screen, so scroll down to see all of the results. 3. Example: tcdf(–1, 2, 25) yields the area between t = - 1 and t = 2, assuming that there are 25 degrees of freedom. HINT The TESTS menu includes confidence interval functions and hypothesis testing functions. Function names ending with Interval (or Int) generate confidence interval limits, but those ending with Test are used for hypothesis tests. FINDING VALUE 1. 2. Press F O for the DISTR (distribution) menu. Select invT, which is used with this format: invT(cumulative area from the left, df) Goodness-of-Fit For the TI-84 Plus only. 1. 2. 3. 4. Enter observed freqs in L1 and expected freqs in L2. Press K, select TESTS, and select X 2 GOF-Test. Enter df (which is 1 less than number of categories). Scroll to Calculate and press [. CONFIDENCE INTERVAL FOR ONE PROPORTION: 1-PROPZINT You must know the number of successes x and the sample size n. Enter the values of x and n, enter a value for the confidence level, such as 0.95, scroll to Calculate and press [. The result will consist of confidence interval limits enclosed within parentheses. 3. 4. 5. 6. Select the first menu item of 1-Var Stats by simply pressing [ (because that option is the default). The screen should display 1-Var Stats, and we must now identify the list to be used for the calculations. Enter the label or name, such as L1 or AGE, then press [. There are more results than can be shown on one screen, so press e to scroll down to the remaining results. Shown below are typical results. HINT Use the format of binom(n, p, x), which corresponds to the binomial probability formula. Example: For 5 degrees of freedom, invT(0.95, 5) yields the t value with an area of 0.95 to its left. Chi-Square Distribution: Finding Area Poisson Distribution 1. 2. Press F O for the DISTR (distribution) menu. Select poissonpdf, which is used with the format of poissonpdf( M , x), where x is the number of successes. 1. 2. 3. Press F O for the DISTR (distribution) menu. Select X 2cdf, which is used with this format: X 2 cdf(lower bound, upper bound, degrees of freedom) Press [ and the area will be displayed. Example: X 2cdf(5, 7, 3) yields the area between 5 and 7 assuming that the number of degrees of freedom is 3. CONFIDENCE INTERVAL ESTIMATE OF p1 - p2: 2-PROPZINT You must know the number of successes x and the sample size n for each of the two samples. Enter those values and enter a value for the confidence level, such as 0.95, scroll to Calculate and press [. The result will consist of confidence interval limits enclosed within parentheses. Example: poissonpdf(0.929, 2) yields the Poisson probability corresponding to m = 0.929 and x = 2. Interpret the results: Sx is the sample standard deviation, and CONFIDENCE INTERVAL FOR ONE MEAN: ZINTERVAL OR TINTERVAL Use TInterval if s is not known (which is the usual case). Inpt: For the first input line labeled Inpt, select Data if you have a list of data values (such as L1 or a named list such as AGE), or select Stats if you know the summary statistics (such as n and x). Make the required entries, scroll to Calculate, then press [. The result will consist of confidence interval limits enclosed within parentheses. sx is the population standard deviation. Introductory statistics courses usually use the sample standard deviation for most applications, so the value of Sx is usually preferred. If the data are summarized in the form of a frequency distribution table, use the following procedure. 1. Enter the class midpoints in list L1. 2. Enter the corresponding class frequencies in list L2. 3. Follow the above six steps for obtaining descriptive statistics from a single list of data, but make this change: In step 5 above, enter L1, L2 (including the comma). Before pressing [ in step 5 above, the screen should display 1-Var Stats L1, L2. 4. Press [ and the results will be displayed. Normal Distribution FINDING AREA To find the area under the curve of a normal probability distribution between two known values: 1. Press F O for the DISTR (distribution) menu. 2. Select normalcdf, which is used with the format normalcdf(lower bound, upper bound, M , S) 3. Press [ and the area will be displayed. Example: normalcdf(80, 105, 100, 15) yields the area between 80 and 105, assuming m = 100 and s = 15. If there is no lower bound or no upper bound, enter a very large number, as indicated below. • Cumulative area from the left with no actual lower bound: Enter –99999999 for the lower bound. • Cumulative area from the right with no actual upper bound: Enter 99999999 for the upper bound. NOTE There is no function for finding a value given an area under a x2 distribution, but a program can be used instead. See, for example, Michael Lloyd’s program X2VAL on the CD-ROM included with the textbook. FROM A FREQUENCY DISTRIBUTION Notes: • Results include P-values but not critical values, so the Pvalue method of hypothesis testing is used. • A line near the bottom of the screen of inputs will include the symbols below. Choose one of them. Z Two-tailed test 6 Left-tailed test 7 Right-tailed test • The last line provides a choice between Calculate (with results displayed) or Draw, which provides a graph with the P-value area shaded. • If given a prompt of Inpt (input) with a choice of Data or Stats, select Data if the data are stored as lists, or select Stats if the summary statistics are already known. • If a prompt of Freq (frequency) is shown, enter 1 to indicate that each sample value occurs once. • 2-SampTTest: If using 2-SampTTest, the prompt of Pooled requires a choice of No or Yes, so choose No if it is not assumed that s1 = s2, but choose Yes if that assumption is made. Recommendation: Select No so that the variances are not pooled. Contingency Table 1. 2. 3. 4. 5. 6. Access the Matrix menu by pressing F Q. (For TI-83, press the key with MATRIX on its face.) Use the arrow keys to select EDIT, then press [. Enter the dimensions of the contingency table, such as 2 * 3, then proceed to enter the table frequencies. Press K, select TESTS, then select X 2-Test. The Observed matrix should be matrix A, consisting of the observed frequencies. Scroll to Calculate and press [. One-Way Analysis of Variance 1. 2. 3. Enter the samples of data as lists, such as L1, L2, L3, or as named lists. Press K, select TESTS, scroll down to ANOVA( and press [. Now enter the list labels or names, separated by commas. Example: If the sample data are in lists L1, L2, L3, enter those lists so that the screen display is ANOVA(L1, L2, L3). Press [ and the results will be displayed. The first two lines show the test statistic F and the P-value. F Distribution: Finding Area 1. 2. 3. Press F O for the DISTR (distribution) menu. Select Fcdf, which is used with this format: Fcdf(lower bound, upper bound, num. df, den. df) Press [ and the area will be displayed. CONFIDENCE INTERVAL ESTIMATE OF M 1 - M 2: 2-SAMPZINT OR 2-SAMPTINT Use 2-SampTInt if s1 and s2 are not known. Inpt: For the first input line labeled Inpt, select Data if you have the two lists of data values (such as L1and L2 or named lists such as AGE1 and AGE2), or select Stats if you know the summary statistics for both samples. Make the required entries and scroll to Calculate, then press [. Note: If using 2-SampTInt, the prompt of Pooled requires a choice of No or Yes, so choose No if it is not assumed that s1 = s2 (so the sample variances are not pooled), but choose Yes if that assumption is made. Recommendation: Select No. Hypothesis Test MATCHED PAIRS To test a claim about the mean difference between matched pairs ( m d), follow these steps: 1. Enter the pairs of data in lists L1 and L2. 2. Create a list of the differences by entering L1 - L2 : L3, which is accomplished by pressing these keys: F 1 c F 2 Y F 3 [. 3. With the differences now stored in list L3, select T-Test. 4. Select the Inpt option of Data, and enter L3 on the line labeled List. 5. The prompt of m0 requests the value to be used for the mean difference, so the typical entry is 0. Press K, use the arrow keys to select TESTS, then scroll down to select 2-SampFTest. HINT 4. Assessing Normality To determine whether sample data appears to come from a normally distributed population, construct a histogram, sort the data and examine the minimum and maximum values to identify outliers, and construct a normal quantile plot: 1. 2. Select the STAT PLOTS menu by pressing F E. Press [. With the Plot1 screen On, use the arrow keys to make the selections in the first screen below, then press B 9. The result will be a normal quantile plot, as in the second screen below. NOTE Programs are available for two-way analysis of variance, multiple regression, and some nonparametric tests. Counting Formulas Factorials For n!, first enter n, then press L and use the arrow keys to select PRB. Select ! and press [ [. Permutations To evaluate nPr, first enter the value of n, then press L and use the arrow keys to select PRB. Select nPr, enter the value of r, then press [. Combinations To evaluate nC r, first enter the value of n, then press L and use the arrow keys to select PRB. Select nCr, enter the value of r, then press [. FINDING VALUE To find the value of x corresponding to a known area of a normal probability distribution, use this procedure: 1. Press F O for the DISTR (distribution) menu. 2. Select invNorm, then proceed to use the cumulative area from the left in this format: invNorm(cumulative area from the left, M , S) 3. Press [ and the value of x will be displayed. Example: With m = 100 and s = 15, the entry of invNorm(0.90, 100, 15) yields the value of x corresponding to an area of 0.90 to its left. This is the 90th percentile. CONFIDENCE INTERVAL FOR M d FROM MATCHED PAIRS 1. 2. 3. TWO VARIANCES Generating Random Data To generate random data, press L and select PRB. • For data from a normal distribution, select randNorm and enter m, s, and sample size n, all separated by commas, as in randNorm(100, 15, 50). • For integers, select randInt and enter the minimum, maximum, and sample size n, all separated by commas, as in randInt(1, 6, 50). To obtain a confidence interval estimate of the mean difference between matched pairs ( md), follow these steps: Enter the pairs of data in lists L1 and L2. Create a list of the differences by entering L1 - L2 : L3 with F 1 c F 2 Y F 3 [. With the differences now stored in list L3, use TInterval as described above. Select the Inpt option of Data, and enter L3 on the line labeled List. Correlation and Regression 1. 2. 3. 4. 5. Enter the paired data in lists (such as L1 and L2, or named lists such as AGE and HT). Press K, select TESTS, then select LinRegTTest. For Xlist, enter the list (such as L1 or AGE) to be used for x. For Ylist, enter the list (such as L2 or HT) to be used for y. For Freq (frequency), enter 1. more➤ HINT On calculators with an M key, run the CtlgHelp App. Select an item from the DISTR menu; press a before pressing [ to see the format. The result will be confidence interval limits for the estimate of md. The instructions and key sequences shown for the TI-84 Plus calculator also apply to the TI-84 Plus Silver Edition, TI-83, TI-83 Plus, and TI-83 Silver Edition. 4 5 6 Triola_GraphRefCard 3/29/06 3:26 PM Page 2 T H E T R I O L A S TAT I S T I C S S E R I E S Descriptive Statistics FROM A LIST OF DATA Use the following procedure to find statistics including the mean, standard deviation, and the fivenumber summary. 1. Enter the data in a list, such as L1. A named list, such as AGE, can also be used. 2. Press K. 3. Use the right or left arrow keys to select the menu item of CALC, as shown in the screen below. TI-83/TI-84 Plus Reference Binomial Distribution 1. 2. Press F O for the DISTR (distribution) menu. The DISTR menu includes these two items: binompdf( Gives binomial probabilities for individual values of x. binomcdf( Gives cumulative probabilities (sum of the probabilities for values from 0 up to and including a desired value of x). Select one of the items from step 2. Both items require an entry of n, p, and an optional entry of x. Examples based on n = 8 and p = 0.4: binompdf(8, 0.4, 3) Provides probability for x = 3 binompdf(8, 0.4) Provides the nine probabilities for x = 0 through x = 8 Student t Distribution FINDING AREA 1. 2. 3. Press F O for the DISTR (distribution) menu. Select tcdf, which is used with this format: tcdf(lower bound, upper bound, df) Press [ and the area will be displayed. Confidence Intervals 1. 2. Press K, then use the arrow keys to select TESTS. Use the arrow keys to scroll to the appropriate confidence interval, then press [. Hypothesis Tests: Proportions and Means 1. 2. Press K, then use the arrow keys to select TESTS. Use the arrow keys to choose the correct test. One proportion: 1-PropZTest Two proportions: 2-PropZTest One mean: Z-Test or T-Test (Use T-Test if s is not known.) Two means: 2-SampZTest or 2-SampTTest (Use 2-SampTTest if s1 and s2 are not known.) Press [. 6. 7. For b & r select the option of Z 0 (for a null hypothesis of H0: r = 0). Scroll down to Calculate and press [. Results include intercept (a) and slope (b) of regression equation and linear correlation coefficient r. Results do not all fit on one screen, so scroll down to see all of the results. 3. Example: tcdf(–1, 2, 25) yields the area between t = - 1 and t = 2, assuming that there are 25 degrees of freedom. HINT The TESTS menu includes confidence interval functions and hypothesis testing functions. Function names ending with Interval (or Int) generate confidence interval limits, but those ending with Test are used for hypothesis tests. FINDING VALUE 1. 2. Press F O for the DISTR (distribution) menu. Select invT, which is used with this format: invT(cumulative area from the left, df) Goodness-of-Fit For the TI-84 Plus only. 1. 2. 3. 4. Enter observed freqs in L1 and expected freqs in L2. Press K, select TESTS, and select X 2 GOF-Test. Enter df (which is 1 less than number of categories). Scroll to Calculate and press [. CONFIDENCE INTERVAL FOR ONE PROPORTION: 1-PROPZINT You must know the number of successes x and the sample size n. Enter the values of x and n, enter a value for the confidence level, such as 0.95, scroll to Calculate and press [. The result will consist of confidence interval limits enclosed within parentheses. 3. 4. 5. 6. Select the first menu item of 1-Var Stats by simply pressing [ (because that option is the default). The screen should display 1-Var Stats, and we must now identify the list to be used for the calculations. Enter the label or name, such as L1 or AGE, then press [. There are more results than can be shown on one screen, so press e to scroll down to the remaining results. Shown below are typical results. HINT Use the format of binom(n, p, x), which corresponds to the binomial probability formula. Example: For 5 degrees of freedom, invT(0.95, 5) yields the t value with an area of 0.95 to its left. Chi-Square Distribution: Finding Area Poisson Distribution 1. 2. Press F O for the DISTR (distribution) menu. Select poissonpdf, which is used with the format of poissonpdf( M , x), where x is the number of successes. 1. 2. 3. Press F O for the DISTR (distribution) menu. Select X 2cdf, which is used with this format: X 2 cdf(lower bound, upper bound, degrees of freedom) Press [ and the area will be displayed. Example: X 2cdf(5, 7, 3) yields the area between 5 and 7 assuming that the number of degrees of freedom is 3. CONFIDENCE INTERVAL ESTIMATE OF p1 - p2: 2-PROPZINT You must know the number of successes x and the sample size n for each of the two samples. Enter those values and enter a value for the confidence level, such as 0.95, scroll to Calculate and press [. The result will consist of confidence interval limits enclosed within parentheses. Example: poissonpdf(0.929, 2) yields the Poisson probability corresponding to m = 0.929 and x = 2. Interpret the results: Sx is the sample standard deviation, and CONFIDENCE INTERVAL FOR ONE MEAN: ZINTERVAL OR TINTERVAL Use TInterval if s is not known (which is the usual case). Inpt: For the first input line labeled Inpt, select Data if you have a list of data values (such as L1 or a named list such as AGE), or select Stats if you know the summary statistics (such as n and x). Make the required entries, scroll to Calculate, then press [. The result will consist of confidence interval limits enclosed within parentheses. sx is the population standard deviation. Introductory statistics courses usually use the sample standard deviation for most applications, so the value of Sx is usually preferred. If the data are summarized in the form of a frequency distribution table, use the following procedure. 1. Enter the class midpoints in list L1. 2. Enter the corresponding class frequencies in list L2. 3. Follow the above six steps for obtaining descriptive statistics from a single list of data, but make this change: In step 5 above, enter L1, L2 (including the comma). Before pressing [ in step 5 above, the screen should display 1-Var Stats L1, L2. 4. Press [ and the results will be displayed. Normal Distribution FINDING AREA To find the area under the curve of a normal probability distribution between two known values: 1. Press F O for the DISTR (distribution) menu. 2. Select normalcdf, which is used with the format normalcdf(lower bound, upper bound, M , S) 3. Press [ and the area will be displayed. Example: normalcdf(80, 105, 100, 15) yields the area between 80 and 105, assuming m = 100 and s = 15. If there is no lower bound or no upper bound, enter a very large number, as indicated below. • Cumulative area from the left with no actual lower bound: Enter –99999999 for the lower bound. • Cumulative area from the right with no actual upper bound: Enter 99999999 for the upper bound. NOTE There is no function for finding a value given an area under a x2 distribution, but a program can be used instead. See, for example, Michael Lloyd’s program X2VAL on the CD-ROM included with the textbook. FROM A FREQUENCY DISTRIBUTION Notes: • Results include P-values but not critical values, so the Pvalue method of hypothesis testing is used. • A line near the bottom of the screen of inputs will include the symbols below. Choose one of them. Z Two-tailed test 6 Left-tailed test 7 Right-tailed test • The last line provides a choice between Calculate (with results displayed) or Draw, which provides a graph with the P-value area shaded. • If given a prompt of Inpt (input) with a choice of Data or Stats, select Data if the data are stored as lists, or select Stats if the summary statistics are already known. • If a prompt of Freq (frequency) is shown, enter 1 to indicate that each sample value occurs once. • 2-SampTTest: If using 2-SampTTest, the prompt of Pooled requires a choice of No or Yes, so choose No if it is not assumed that s1 = s2, but choose Yes if that assumption is made. Recommendation: Select No so that the variances are not pooled. Contingency Table 1. 2. 3. 4. 5. 6. Access the Matrix menu by pressing F Q. (For TI-83, press the key with MATRIX on its face.) Use the arrow keys to select EDIT, then press [. Enter the dimensions of the contingency table, such as 2 * 3, then proceed to enter the table frequencies. Press K, select TESTS, then select X 2-Test. The Observed matrix should be matrix A, consisting of the observed frequencies. Scroll to Calculate and press [. One-Way Analysis of Variance 1. 2. 3. Enter the samples of data as lists, such as L1, L2, L3, or as named lists. Press K, select TESTS, scroll down to ANOVA( and press [. Now enter the list labels or names, separated by commas. Example: If the sample data are in lists L1, L2, L3, enter those lists so that the screen display is ANOVA(L1, L2, L3). Press [ and the results will be displayed. The first two lines show the test statistic F and the P-value. F Distribution: Finding Area 1. 2. 3. Press F O for the DISTR (distribution) menu. Select Fcdf, which is used with this format: Fcdf(lower bound, upper bound, num. df, den. df) Press [ and the area will be displayed. CONFIDENCE INTERVAL ESTIMATE OF M 1 - M 2: 2-SAMPZINT OR 2-SAMPTINT Use 2-SampTInt if s1 and s2 are not known. Inpt: For the first input line labeled Inpt, select Data if you have the two lists of data values (such as L1and L2 or named lists such as AGE1 and AGE2), or select Stats if you know the summary statistics for both samples. Make the required entries and scroll to Calculate, then press [. Note: If using 2-SampTInt, the prompt of Pooled requires a choice of No or Yes, so choose No if it is not assumed that s1 = s2 (so the sample variances are not pooled), but choose Yes if that assumption is made. Recommendation: Select No. Hypothesis Test MATCHED PAIRS To test a claim about the mean difference between matched pairs ( m d), follow these steps: 1. Enter the pairs of data in lists L1 and L2. 2. Create a list of the differences by entering L1 - L2 : L3, which is accomplished by pressing these keys: F 1 c F 2 Y F 3 [. 3. With the differences now stored in list L3, select T-Test. 4. Select the Inpt option of Data, and enter L3 on the line labeled List. 5. The prompt of m0 requests the value to be used for the mean difference, so the typical entry is 0. Press K, use the arrow keys to select TESTS, then scroll down to select 2-SampFTest. HINT 4. Assessing Normality To determine whether sample data appears to come from a normally distributed population, construct a histogram, sort the data and examine the minimum and maximum values to identify outliers, and construct a normal quantile plot: 1. 2. Select the STAT PLOTS menu by pressing F E. Press [. With the Plot1 screen On, use the arrow keys to make the selections in the first screen below, then press B 9. The result will be a normal quantile plot, as in the second screen below. NOTE Programs are available for two-way analysis of variance, multiple regression, and some nonparametric tests. Counting Formulas Factorials For n!, first enter n, then press L and use the arrow keys to select PRB. Select ! and press [ [. Permutations To evaluate nPr, first enter the value of n, then press L and use the arrow keys to select PRB. Select nPr, enter the value of r, then press [. Combinations To evaluate nC r, first enter the value of n, then press L and use the arrow keys to select PRB. Select nCr, enter the value of r, then press [. FINDING VALUE To find the value of x corresponding to a known area of a normal probability distribution, use this procedure: 1. Press F O for the DISTR (distribution) menu. 2. Select invNorm, then proceed to use the cumulative area from the left in this format: invNorm(cumulative area from the left, M , S) 3. Press [ and the value of x will be displayed. Example: With m = 100 and s = 15, the entry of invNorm(0.90, 100, 15) yields the value of x corresponding to an area of 0.90 to its left. This is the 90th percentile. CONFIDENCE INTERVAL FOR M d FROM MATCHED PAIRS 1. 2. 3. TWO VARIANCES Generating Random Data To generate random data, press L and select PRB. • For data from a normal distribution, select randNorm and enter m, s, and sample size n, all separated by commas, as in randNorm(100, 15, 50). • For integers, select randInt and enter the minimum, maximum, and sample size n, all separated by commas, as in randInt(1, 6, 50). To obtain a confidence interval estimate of the mean difference between matched pairs ( md), follow these steps: Enter the pairs of data in lists L1 and L2. Create a list of the differences by entering L1 - L2 : L3 with F 1 c F 2 Y F 3 [. With the differences now stored in list L3, use TInterval as described above. Select the Inpt option of Data, and enter L3 on the line labeled List. Correlation and Regression 1. 2. 3. 4. 5. Enter the paired data in lists (such as L1 and L2, or named lists such as AGE and HT). Press K, select TESTS, then select LinRegTTest. For Xlist, enter the list (such as L1 or AGE) to be used for x. For Ylist, enter the list (such as L2 or HT) to be used for y. For Freq (frequency), enter 1. more➤ HINT On calculators with an M key, run the CtlgHelp App. Select an item from the DISTR menu; press a before pressing [ to see the format. The result will be confidence interval limits for the estimate of md. The instructions and key sequences shown for the TI-84 Plus calculator also apply to the TI-84 Plus Silver Edition, TI-83, TI-83 Plus, and TI-83 Silver Edition. 4 5 6 Triola_GraphRefCard 3/29/06 3:26 PM Page 2 T H E T R I O L A S TAT I S T I C S S E R I E S Descriptive Statistics FROM A LIST OF DATA Use the following procedure to find statistics including the mean, standard deviation, and the fivenumber summary. 1. Enter the data in a list, such as L1. A named list, such as AGE, can also be used. 2. Press K. 3. Use the right or left arrow keys to select the menu item of CALC, as shown in the screen below. TI-83/TI-84 Plus Reference Binomial Distribution 1. 2. Press F O for the DISTR (distribution) menu. The DISTR menu includes these two items: binompdf( Gives binomial probabilities for individual values of x. binomcdf( Gives cumulative probabilities (sum of the probabilities for values from 0 up to and including a desired value of x). Select one of the items from step 2. Both items require an entry of n, p, and an optional entry of x. Examples based on n = 8 and p = 0.4: binompdf(8, 0.4, 3) Provides probability for x = 3 binompdf(8, 0.4) Provides the nine probabilities for x = 0 through x = 8 Student t Distribution FINDING AREA 1. 2. 3. Press F O for the DISTR (distribution) menu. Select tcdf, which is used with this format: tcdf(lower bound, upper bound, df) Press [ and the area will be displayed. Confidence Intervals 1. 2. Press K, then use the arrow keys to select TESTS. Use the arrow keys to scroll to the appropriate confidence interval, then press [. Hypothesis Tests: Proportions and Means 1. 2. Press K, then use the arrow keys to select TESTS. Use the arrow keys to choose the correct test. One proportion: 1-PropZTest Two proportions: 2-PropZTest One mean: Z-Test or T-Test (Use T-Test if s is not known.) Two means: 2-SampZTest or 2-SampTTest (Use 2-SampTTest if s1 and s2 are not known.) Press [. 6. 7. For b & r select the option of Z 0 (for a null hypothesis of H0: r = 0). Scroll down to Calculate and press [. Results include intercept (a) and slope (b) of regression equation and linear correlation coefficient r. Results do not all fit on one screen, so scroll down to see all of the results. 3. Example: tcdf(–1, 2, 25) yields the area between t = - 1 and t = 2, assuming that there are 25 degrees of freedom. HINT The TESTS menu includes confidence interval functions and hypothesis testing functions. Function names ending with Interval (or Int) generate confidence interval limits, but those ending with Test are used for hypothesis tests. FINDING VALUE 1. 2. Press F O for the DISTR (distribution) menu. Select invT, which is used with this format: invT(cumulative area from the left, df) Goodness-of-Fit For the TI-84 Plus only. 1. 2. 3. 4. Enter observed freqs in L1 and expected freqs in L2. Press K, select TESTS, and select X 2 GOF-Test. Enter df (which is 1 less than number of categories). Scroll to Calculate and press [. CONFIDENCE INTERVAL FOR ONE PROPORTION: 1-PROPZINT You must know the number of successes x and the sample size n. Enter the values of x and n, enter a value for the confidence level, such as 0.95, scroll to Calculate and press [. The result will consist of confidence interval limits enclosed within parentheses. 3. 4. 5. 6. Select the first menu item of 1-Var Stats by simply pressing [ (because that option is the default). The screen should display 1-Var Stats, and we must now identify the list to be used for the calculations. Enter the label or name, such as L1 or AGE, then press [. There are more results than can be shown on one screen, so press e to scroll down to the remaining results. Shown below are typical results. HINT Use the format of binom(n, p, x), which corresponds to the binomial probability formula. Example: For 5 degrees of freedom, invT(0.95, 5) yields the t value with an area of 0.95 to its left. Chi-Square Distribution: Finding Area Poisson Distribution 1. 2. Press F O for the DISTR (distribution) menu. Select poissonpdf, which is used with the format of poissonpdf( M , x), where x is the number of successes. 1. 2. 3. Press F O for the DISTR (distribution) menu. Select X 2cdf, which is used with this format: X 2 cdf(lower bound, upper bound, degrees of freedom) Press [ and the area will be displayed. Example: X 2cdf(5, 7, 3) yields the area between 5 and 7 assuming that the number of degrees of freedom is 3. CONFIDENCE INTERVAL ESTIMATE OF p1 - p2: 2-PROPZINT You must know the number of successes x and the sample size n for each of the two samples. Enter those values and enter a value for the confidence level, such as 0.95, scroll to Calculate and press [. The result will consist of confidence interval limits enclosed within parentheses. Example: poissonpdf(0.929, 2) yields the Poisson probability corresponding to m = 0.929 and x = 2. Interpret the results: Sx is the sample standard deviation, and CONFIDENCE INTERVAL FOR ONE MEAN: ZINTERVAL OR TINTERVAL Use TInterval if s is not known (which is the usual case). Inpt: For the first input line labeled Inpt, select Data if you have a list of data values (such as L1 or a named list such as AGE), or select Stats if you know the summary statistics (such as n and x). Make the required entries, scroll to Calculate, then press [. The result will consist of confidence interval limits enclosed within parentheses. sx is the population standard deviation. Introductory statistics courses usually use the sample standard deviation for most applications, so the value of Sx is usually preferred. If the data are summarized in the form of a frequency distribution table, use the following procedure. 1. Enter the class midpoints in list L1. 2. Enter the corresponding class frequencies in list L2. 3. Follow the above six steps for obtaining descriptive statistics from a single list of data, but make this change: In step 5 above, enter L1, L2 (including the comma). Before pressing [ in step 5 above, the screen should display 1-Var Stats L1, L2. 4. Press [ and the results will be displayed. Normal Distribution FINDING AREA To find the area under the curve of a normal probability distribution between two known values: 1. Press F O for the DISTR (distribution) menu. 2. Select normalcdf, which is used with the format normalcdf(lower bound, upper bound, M , S) 3. Press [ and the area will be displayed. Example: normalcdf(80, 105, 100, 15) yields the area between 80 and 105, assuming m = 100 and s = 15. If there is no lower bound or no upper bound, enter a very large number, as indicated below. • Cumulative area from the left with no actual lower bound: Enter –99999999 for the lower bound. • Cumulative area from the right with no actual upper bound: Enter 99999999 for the upper bound. NOTE There is no function for finding a value given an area under a x2 distribution, but a program can be used instead. See, for example, Michael Lloyd’s program X2VAL on the CD-ROM included with the textbook. FROM A FREQUENCY DISTRIBUTION Notes: • Results include P-values but not critical values, so the Pvalue method of hypothesis testing is used. • A line near the bottom of the screen of inputs will include the symbols below. Choose one of them. Z Two-tailed test 6 Left-tailed test 7 Right-tailed test • The last line provides a choice between Calculate (with results displayed) or Draw, which provides a graph with the P-value area shaded. • If given a prompt of Inpt (input) with a choice of Data or Stats, select Data if the data are stored as lists, or select Stats if the summary statistics are already known. • If a prompt of Freq (frequency) is shown, enter 1 to indicate that each sample value occurs once. • 2-SampTTest: If using 2-SampTTest, the prompt of Pooled requires a choice of No or Yes, so choose No if it is not assumed that s1 = s2, but choose Yes if that assumption is made. Recommendation: Select No so that the variances are not pooled. Contingency Table 1. 2. 3. 4. 5. 6. Access the Matrix menu by pressing F Q. (For TI-83, press the key with MATRIX on its face.) Use the arrow keys to select EDIT, then press [. Enter the dimensions of the contingency table, such as 2 * 3, then proceed to enter the table frequencies. Press K, select TESTS, then select X 2-Test. The Observed matrix should be matrix A, consisting of the observed frequencies. Scroll to Calculate and press [. One-Way Analysis of Variance 1. 2. 3. Enter the samples of data as lists, such as L1, L2, L3, or as named lists. Press K, select TESTS, scroll down to ANOVA( and press [. Now enter the list labels or names, separated by commas. Example: If the sample data are in lists L1, L2, L3, enter those lists so that the screen display is ANOVA(L1, L2, L3). Press [ and the results will be displayed. The first two lines show the test statistic F and the P-value. F Distribution: Finding Area 1. 2. 3. Press F O for the DISTR (distribution) menu. Select Fcdf, which is used with this format: Fcdf(lower bound, upper bound, num. df, den. df) Press [ and the area will be displayed. CONFIDENCE INTERVAL ESTIMATE OF M 1 - M 2: 2-SAMPZINT OR 2-SAMPTINT Use 2-SampTInt if s1 and s2 are not known. Inpt: For the first input line labeled Inpt, select Data if you have the two lists of data values (such as L1and L2 or named lists such as AGE1 and AGE2), or select Stats if you know the summary statistics for both samples. Make the required entries and scroll to Calculate, then press [. Note: If using 2-SampTInt, the prompt of Pooled requires a choice of No or Yes, so choose No if it is not assumed that s1 = s2 (so the sample variances are not pooled), but choose Yes if that assumption is made. Recommendation: Select No. Hypothesis Test MATCHED PAIRS To test a claim about the mean difference between matched pairs ( m d), follow these steps: 1. Enter the pairs of data in lists L1 and L2. 2. Create a list of the differences by entering L1 - L2 : L3, which is accomplished by pressing these keys: F 1 c F 2 Y F 3 [. 3. With the differences now stored in list L3, select T-Test. 4. Select the Inpt option of Data, and enter L3 on the line labeled List. 5. The prompt of m0 requests the value to be used for the mean difference, so the typical entry is 0. Press K, use the arrow keys to select TESTS, then scroll down to select 2-SampFTest. HINT 4. Assessing Normality To determine whether sample data appears to come from a normally distributed population, construct a histogram, sort the data and examine the minimum and maximum values to identify outliers, and construct a normal quantile plot: 1. 2. Select the STAT PLOTS menu by pressing F E. Press [. With the Plot1 screen On, use the arrow keys to make the selections in the first screen below, then press B 9. The result will be a normal quantile plot, as in the second screen below. NOTE Programs are available for two-way analysis of variance, multiple regression, and some nonparametric tests. Counting Formulas Factorials For n!, first enter n, then press L and use the arrow keys to select PRB. Select ! and press [ [. Permutations To evaluate nPr, first enter the value of n, then press L and use the arrow keys to select PRB. Select nPr, enter the value of r, then press [. Combinations To evaluate nC r, first enter the value of n, then press L and use the arrow keys to select PRB. Select nCr, enter the value of r, then press [. FINDING VALUE To find the value of x corresponding to a known area of a normal probability distribution, use this procedure: 1. Press F O for the DISTR (distribution) menu. 2. Select invNorm, then proceed to use the cumulative area from the left in this format: invNorm(cumulative area from the left, M , S) 3. Press [ and the value of x will be displayed. Example: With m = 100 and s = 15, the entry of invNorm(0.90, 100, 15) yields the value of x corresponding to an area of 0.90 to its left. This is the 90th percentile. CONFIDENCE INTERVAL FOR M d FROM MATCHED PAIRS 1. 2. 3. TWO VARIANCES Generating Random Data To generate random data, press L and select PRB. • For data from a normal distribution, select randNorm and enter m, s, and sample size n, all separated by commas, as in randNorm(100, 15, 50). • For integers, select randInt and enter the minimum, maximum, and sample size n, all separated by commas, as in randInt(1, 6, 50). To obtain a confidence interval estimate of the mean difference between matched pairs ( md), follow these steps: Enter the pairs of data in lists L1 and L2. Create a list of the differences by entering L1 - L2 : L3 with F 1 c F 2 Y F 3 [. With the differences now stored in list L3, use TInterval as described above. Select the Inpt option of Data, and enter L3 on the line labeled List. Correlation and Regression 1. 2. 3. 4. 5. Enter the paired data in lists (such as L1 and L2, or named lists such as AGE and HT). Press K, select TESTS, then select LinRegTTest. For Xlist, enter the list (such as L1 or AGE) to be used for x. For Ylist, enter the list (such as L2 or HT) to be used for y. For Freq (frequency), enter 1. more➤ HINT On calculators with an M key, run the CtlgHelp App. Select an item from the DISTR menu; press a before pressing [ to see the format. The result will be confidence interval limits for the estimate of md. The instructions and key sequences shown for the TI-84 Plus calculator also apply to the TI-84 Plus Silver Edition, TI-83, TI-83 Plus, and TI-83 Silver Edition. 4 5 6 ...
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