Attached is a recent printout of weights from 2100 tablets recently manufactured.

**Complete the activities and questions below: **

1. How realistic do you think it is to use all the data in order to calculate the percentage of tablets that are in the ideal weight range, as well as, determine the mean weight?

2. If not all the data is used to calculate ideal weight range and mean weight, how many data values of the tablets do you feel would give you enough information to provide a relatively close representation of the entire list?

3. Describe a method for choosing the number of data values you specified in question #2.

4. Using the data of the manufactured tablets, circle or highlight the data values that are aligned with the number and method described in questions #2 and #3 respectively.

5. Open an Excel spreadsheet and enter the data values that you circled or highlighted.

6. Find the mean of this group of data.

a. Mean =

7. Determine how many in your list are in the target zone (595 - 605)

a. Number in target zone =

b. Percentage in target zone =

8. Based on your results, does this fail either of the two benchmarks (less than 90% in the target range or a mean not between 597-603)?

9. Since you only chose a fraction of the data, how confident (use the scale below) are you that these numbers accurately portray the entire data?

Scale: (1) Not confident at all - - **to - - ** (5) Very confident

10. Finally, would you request the manufacturing process be shut down to make necessary changes?

**Confidence Interval Application: **

11. Write down your answers from question #6 and #7.

a. Mean of data =

b. Percent in target range =

As discussed in class, since you only chose a sample of **all** data values, these numbers aren't exact, but hopefully close. Hopefully?!

12. Using the two confidence interval formulas discussed in the narrated PowerPoints, determine the range of values that are 95% confidence the actual mean or within the target range the entire set of data is between.

a. 95% Confident the mean range is =

b. 95% Confident the percentage within the target range is =

13. Using the two confidence interval formulas, complete the same steps for a 99.7% confidence interval.

a. 99.7% Confident the mean range is =

b. 99.7% Confident the percentage within the target range is =

14. Do these results change how you would answer the question: Should you shut down the production process? Explain your reasoning.

**Changes Over Time Analysis: **

Besides an overall concern of the manufacturing process, there is also concern of how the manufacturing process changes over time. For example, is the process good in the beginning, but progressively gets worse as more tablets are produced? In this case, it may even out. Good at the beginning and bad in the end may result in adequate overall.

For this analysis, you will look at the first third of the data values, the middle third of the data values, and the last third of the data values. To make this simple, divide the pages by thirds- the first third will be page 1, middle third page 2, and last third, page 3.

15. You will not use all data values for each of these. Determine how many from each of the 3 sections you will want and a method by which to choose them. Put your selected values in an excel spreadsheet. Analyze these values and determine if there is any difference between the beginning of the production process, the middle, and the end.

*Note:* Don't rely solely on the values for the mean and percentage in the range. Do a 95% confidence interval (mean and % in range) for each of these as this will help you make a more accurate judgment as to how the three compare.

16. Comment on how you view the production process over time. Support your conclusions with the results of your calculations.

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