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Unformatted text preview: \J $131211 Quill Name Fall 1993 Fill inthe blank with anappropriate word. 1. E’s} 10. The entire collection of individuals or objects about which information is desired is called the 3 {2' 1'2} , lék‘l] Q t- } of interest. A {.13 3! '13 .l 1 “7.3.53! .4 study. The method ofsampling that will be utilized in our class is known as random sampling. . is a subset of the population selected in some prescribed manner for Statistical methods that organize and summarize data for etTective presentation and increased understanding are called '“ " ' -- ‘ " statistical methods. Statistical methods designed to make generalizations about the population from which the sample was collected based only on the information in the sample are called statistical methods. .2;: f Our authors discuss two types of data. The data which results from asking the question "What brand of shoes are you currently wearing?" would be classified as géflfi 9gp . g £31 data. A mm Mifi V is a quantity that describes some characteristic of the population is a quantity that describes some characteristic of the sample. Our authors discuss discrete and continuous data. The data which results from recording "the ntrmberofphone calls per day to the emergency number 911' is an example of ”i ‘5; g r data. The list of objects fiom which we select our sampling units is called the sampling 3 . g ‘3 33 " . Statlll QuizZ Name w 6" Fall 1993 \_/ Circle the letter T if the statement is always true, otherwise circle F. a. I. T F For any data set, the sum of the squared deviations from the mean is zero. _I\J @ F Of the three measures of location (mean. median, mode), the median is the measure which is least sensitive to (affected by) extreme values. 3. T (F; The sample standard deviation is designated by the symbol 0’. 4. (1") F The population variance is a parameter. 5' T ‘@ When calculating a 10% trimmed mean. you actually find the mean of 90% of the data ' values. , ,.., V! 6. T B The "empirical rule" is applicable only to any data set. F One of the nice characteristics of the standard deviation is that it is in the same unit of measurement as the original data values. a, o/S. T F The 2 score associated with an observation tells us how many standard deviations the observation is from the mean and whether the observation is above or below the mean. V 9. - ® F The rth percentile is a value (number) such that r percent of the observations in the data set fall at or below that value. l0. T F The quantities 2x2 and (20:)2 represent the same thing and therefore will have the same ” numerical value. Stat 211 I Quiz 3 Name Fall 1993 E—r Answer a question as true (T) if it is always true: otherwise answer (F). 1. l A simple event is an event consisting of exactly one outcome. 2. l The event (A orBi consists of all experimental outcomes that are in both A and B. The only requirement for the probabilities that we assign to the points in the .sample space is that the probabilities sum to one. “ 3. 13 4. T If two events E. F are mutually exclusive then they are dependent. 5. I The probability of an event E. denoted by P(E), is the value approached by the relative frequency of occurrence of E in a very long series of replications of a chance experiment. 6. An event A and its complement (not A) are always dependent events. 7. For any event. the probability of that event is equal to the ratio of "the number of outcomes in E" to "the number of possible outcomes for the experiment". 4/ 8. if P(E | F) is a notation that means P(E) divided by P(F). ‘-—I 9. i A numerical variable whose value depends on the outcome of a chance experiment is called a random variable. 10. l The probability distribution of a discrete random variable x gives the probability associated with each possible it value. Stat 21 1 Quiz 4 Fall 1993 Name For questions 1 through 5 fill in the blanks. l. The tho major categories of random variables are @132: rm. and 1'2.‘7;E-fl - u u H n w i 3 "WV-'8 .. I . 2. The "number of defective tires on a car 13 an example of a I“. t"; 1 'f ‘t -' random variable. 3. The probability {i I i "ii 0 RV of a random variable gives the probability associated with each possible x-value. (an. F 4. The two symbols used to denote the expected value of X are LL and , .-":_ UI 3! has a numerical value of (i . In questions 6 through 8. answer true (T) or false (F). I 6. i l The expected value of a random variable is the value of the random variable we expect to occur when the experiment is performed. 7. g F The expected value of a random variable X is the most probable value of X. 8. I In a binomial experiment. the random variable counts the number of successes that occur in a fixed number of replications or trials. 9. List the four properties of a binomial experiment. A, .. ,- , « ‘- . t ‘ ,.. . ,r- . ' 5W” ' - .-... -’= . .t ' a. ‘ S i“- ‘34 : l i . ~ . - p ‘ = .x - .- - _ l ._v . t. - ., . . . t... Stat Ell Fall1993 V Quiz 5 Name Answer each of the following as true (T) or false (F). I lquantity tfl ti 9. % i The larger the variance of the population being sampled. the larger the variance of the To standardized a random variable, one subtraCts the mean from the random variable and divides that difference by the standard deviatiOn. The symbol tti den0tes the mean of all possible sample means of a specified size taken from a population. It is always true that up = it. The standard deviation 0'? is often referred to as the standard error of the mean. The Central Limit Theorem implies that the disrribution of the sample mean will be approximately normally distributed even when n is small. A consequence of the Central Limit Theorem is that the distribution of the random 2—1.1? K is approximately a standard normal. The two symbols Hg and ER) represent the some thing. A statistic with mean value equal to the value of the population characterisric being estimated is said to be an unbiased statistic. sampling distribution of the sample mean. 10. i Ti" based on a large It tends to be closer to _Lt than does I based on a small n. W . m“ /\C- - _ <, 3;“, tack-r V d \\‘ “(J «a t /\’7/ /b /7 -/ Stat211 Exam 1 Name Fall 1993 Instructions: This is a closed book examination. You may use the formula sheet from your packet. You may also use a calculator. but you must show sufficient work in order for me to evaluate the process whereby you arrived at your answer. Submit your solutions in an 8.5 X 11 blue-book. Please start each major problem on a new page and please leave space for me to write comments or corrections. The seven problems are worth 20. 16. 10. 8. 20. 16. and 10 points. respectively. 1. The following stern and leaf display shows grade point averages for a random sample of students. . *4 Stem Leaf 1 5 9 stem: ones 2 0122279 leaf: tenths 3 2 3 4 6 7 9' 4 0 . '. . , , f ’ . .4 “Pi . ' - . - {IA-)1!“ . - v 7 ".5 a) How many observations are in the data set? ' b) What is the median of the data set? c) What is the mode of the data set? (1 ‘ What is the range of the data set? e) Compute an estimate of the sample standard deviation. 3. Do not calculate the sample standard deviation by using the fonnula for s. [Hintz Consider making use of your answer to part ((1).) 2. The following is set of exam scores. \ - l ’\ _\ X \ [my . ‘. 25 26 39 48 asks 8a 2 9\6\s1 its at 9K”. 90 9093 95 99 99. 4., The sum of the data values i .473” d the sum of the squares of the data values is(118.755. S a) Compute the value of the sample mean. b) Compute the value of the 10% trimmed mean. C) Compute the value of the sample standard deviation. 3. Suppose that the deviations from the mean for a data set are —5. 0. 3. 1. 6. ~2. —3. Compute the value of the sample standard deviation. In order to construct a frequency distribution and it's associated histogram. one must first define the classes. Using the data below. define classes for a frequency distribution. Be sure to explain why or how you are making the choice that are being made. (You do not have to tally the frequencies for the classes. just set up the class descriptions) 12.8 12.9 13.4 13.4 13.6 13.7 13.9 13.9 14.0 14.1 14.2 14.4 14.5 14.5 14.6 14.6 14.8 14.9 14.9 14.9 15.0 15.1 15.3 15.4 15.4 15.6 15.7 15.9 16.0 16.3 16.4 16.4 16.8 16.9 17.0 17.7 17.7 17.8 18.2 18.3 18.5 18.6 18.7 19.4 21.6 24.0 25.2 29.8. A real-estate multiple listing service for our county recently released a report which gave information about the time required for homes to sell. The report stated that the mean number of weeks that it took for homes to sell was 9.4 weeks and the standard deviation was 5.84 weeks. a) What is the z-score associated with the x-value of 0? b) Consider the values given for the mean and standard deviation and the z-score you computed in partta). Is it plausible for the variable "time to sell home (in weeks)" to possess a mound-shape distribution? Justify your response. v c) What proportion of homes sold more than 24 weeks after they were put up for sale? d) Which measure of location (mean. median. mode. trimmed mean) do you think would best describe the ”typical time required for a home to sell? Why! cl Suppose you are told that 5 weeks is the 25m percentile. What does this mean! ,A I .. . a.“ :"< .t: : : 4 b) C) /8 -—-—-' Customers at a certain department store pay for purchases either with cash or with one of four types of credit card. Store records indicate that 30% ot‘ail purchases involve cash. 25% are made with the store's own credit card. [8% with Mastercard. 15% with Visa. and the remaining 12% of purchases with an American Express card. The accompanying table displays the probabilities of the simple events for the experiment in which the mode of payment for the next transaction is observed. —————-—_____.__—___—_—_ Mode of pavment Cash Store card MC V AE Simple event 01 O2 03 ._ .. 04 05 Probability .30 25 .18 . £5 12 . . Let E be the event that the next purchase is made with a nationally distributed credit card. Compute P(E). Compute P(not E). Let F be the event that the next purchase is made with either the store card or the Mastercard. Compute PtF). Compute P(E or F). A college library has four copies of a certain book: the copies are numbered 1. 3. 3. and 4. Two of these are randomly selected (using slips of paper). The first book selected will be placed on two-hour reserve. and the second one may be checked out on an overnight basisi Construct a tree diagram to display the 12 outcomes in the sample space. Let A denote the event that at least one of the books selected is an even-numbered copy. What outcomes are in A? Suppose copies 1 and 2 are first printings. whereas copies 3 and 4 are second printings. Let B denote the event that exactly one of the copies selected is a first printing. What outcomes are contained in B? Stat ‘21l Exam 2 Name __—_s—__ Instructions: This is a closed book examination. You may use the formula sheets and the tables from your packet. You may also use a calculator\ however. sufficient work needs to be shown so that I can evaluate your work. Submit your work in an 8.5 by ll blue-book. The point values for the problems. respectively. are 20.10,5,20. ll}. 10. 15. and 10. 1. Let Z denote a random variable having a standard normal distribution. a) \Vhat is the mean value of 2.? What. is the standard deviation of Z? b) Determine the value of P(Z < —l.23). c) Determine the value of P(l.l4< Z S 3.04]. d) Determine the value of P(Z 2 —0.28). e) Determine the number c such that P(—r: E Z S c): .1373. he time that it takes a randomly selected job applicant to perform a certain task is normally distributed with a mean value 0f120 sec and a standard deviation of 20 sec. The fastest lU‘7c are to be given advanced training. What task limes qualify individuals for such training.P .‘3. A manufacturer of electrical toasters ships them in boxes. with 2-1 in each box. Periodically. three toasters are selected from a box and each is examined for defects. Let X equal the number of defective toasters in the sample of n 2 3. Explain why X is or is not a binomial random variable. 4. A manufacturer of cellular phones claims that no more than 5% of its product are defective. Suppose that the manufacturer's Claim is true and that the proportion defective in all cellular phones made by this company is five percent. a) lfyou receive ashipnient of n = '25 cellular phones produced by this company, what is the probability I that more than one will be defective? b) “that is the expected number of defective phones per shipment? c] What is the standard deViation of number of defective phones per shipment? d)‘ \Vhat is the probability that the number of defective phones will be within one standard deviation of the mean number of defective phones? .), Answer question -la if the shipment had contained only T phones rather then 25. 6. A personal computer salesperson working on a commission receives a fixed amount for each system sold. [ha Suppose that for a given month. the probability distibntion of x = the number of systems sold is gw‘jn l in the accompanying table. I‘V '0 \\ Ii} .5"?! ' a». U . num— -n- id the mean number of systems sold. iat is the probability that x is within 2 of its mean value? :OVERl 7‘ The probability that a randomly selected customer at a certain gas station checks the oil level is .10. The probability that randomly selected customer checks tire pressure is .04. The probability that a randomly selected customer checks both oil level and tire pressure is .008. a] Given that a customer checks the oil level, what is the probability that the customer checks tire pressure? b) If a randomly selected customer checks tire pressure. what is probability that the oil level is checked also? c] Are the events "checks oil level" and "checks tire pressure" independent? Explain .Let )2 denote the amount of gravel sales (Ions) during a randomly selected week at a particular sales facility. Suppose that the density curve has height flx) above the value x. where {Ml—x) 0<x<l flxl = 0 otherwise Calculate P(.3 S r < .6) llint: Sketch the graph of the density function l'lxl. ...
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