• Homework is due by 5:00 PM on the due date at your course instructor's office. You can always hand in your homework at the end of lecture on Monday.
• You may talk with others about the homework problems but please write your solutions up independently.
• Please answer homework questions in complete sentences. Make sure to staple the pages of your assignment together. Be sure to indicate your lab section on your paper.
• You will have an opportunity to get help on homework during lab.

Reading:    Nov. 30  - Dec.  5   Section  7.2
            Dec.  7  - Dec. 10   Chapter  8.1

1. For each of the following situations, indicate whether it is a two sample problem or a matched pairs problem. Explain briefly your choice. Also indicate whether you would construct a confidence interval or perform a test of the hypothesis and explain your choice.
   • (a) A study is conducted to determine whether taking an ACT preparation course improves the overall score on the ACT. A random sample of high school seniors from a school district is selected and each student is given the ACT. The students then go through an intense six week preparation course. At the end of the six weeks, the students are again given the ACT. The school district would like to determine if there is a significant increase in mean ACT scores after completing the preparation course.

   • (b) Over the years, the game show Jeopardy has had more male winners than female winners. One explanation for this occurrence could be a difference in the reaction times between men and women (men buzz in faster than women). A random sample of 15 previous men contestants and a random sample of 15 previous women contestants are selected and a test of reaction times is given. The show's producers would like to determine if the mean reaction time of women is slower than the mean reaction time of men.

   • (c) The effectiveness of a weight loss program that combines exercise and diet is to be evaluated. Thirty volunteers are weighed before beginning the program and re-weighed after following the program for three months. One wishes to estimate, with 95% confidence, the mean difference between the post-program and pre-program weights.

   • Computers are often compared by running a set of benchmark programs and recording the CPU time required to complete each program. Six benchmark programs are selected. Each program is run on two computers and the CPU times recorded. One wishes to estimate, with 98% confidence the mean difference in CPU times for the two computers.

2. Makers of generic drugs must show that they do not differ significantly from the reference drug that they imitate. One aspect in which drugs might differ in their extent of absorption in the blood. Ten subjects were chosen at random and given both the generic drug and the reference drug. To eliminate bias in the results, five subjects were randomly assigned to take the reference drug first, while the other five subjects were randomly assigned to take the generic drug first. In all cases, a washout period separated the two drugs, so that the first drug taken had disappeared from the blood before the second drug was administered. The drug levels for both the generic and reference drug for each subject are given below.

   
   Subject       1     2     3     4     5     6     7     8     9    10 
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   Reference   4108  2526  2779  3852  1833  2344  1864  1022  2256   938
   Generic     1755  1138  1613  2254  1310  2738  2302  1284  3052  1287
   -----------------------------------------------------------------------
   
   

   • (a) This is an example of a matched pairs experiment. Explain why. \item Calculate the mean difference in absorption rates between the reference and generic drug.

   • (b) Perform a test of hypothesis to determine if the two drugs differ significantly in absorption rates. Use a significance level of 0.05. (The value of the sample standard deviation from the data is 1081.54).

3. Advertisements claim that Happy's Joes puts more pepperoni on its pizzas than competitors. In order to investigate this claim, 9 medium pizzas from Happy Joe's and 9 medium pizzas from Pizza Hut are purchased at random times over a month long period. The number of slices of pepperoni on each pizza is then counted. Below are the data.

   
   (1) Happy Joe's |  43   51   53   49   39   45   56   44  52 | Xbar1=48  
                   |                                            | s1 = 5.55
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                   |                                            |
   (2) Pizza Hut   |  47   33   37   43   28   36   35   35  39 | Xbar2=37  
                   |                                            | s2 = 5.55
   
   

   • (a) Construct a back-to-back stem and leaf plot to compare the two pizza parlors. Describe what you see.

   • (b) Does Happy Joe's have more pepperoni, on average, than Pizza Hut? Perform the appropriate statistical test of hypothesis. Be sure to comment on the truthfulness of Happy Joe's advertising, based on your test.

   • (c) Construct a 90% confidence interval for the difference between the mean number of slices of pepperoni per medium pizza.

4. A random sample of 20 students, 10 girls and 10 boys, is taken in a Midwest school district. The mean IQ score for the 10 girls is 103.6 with a standard deviation of 8.91. The mean IQ score for the 10 boys is 107 with a standard deviation of 5.58.
   • (a) Calculate a 95% confidence interval for the difference between the population mean IQ score for boys and the population mean IQ score for girls from this school district.

   • (b) We would like to test whether the two population mean IQ scores are different. The null and alternative hypotheses for this test are Ho: mu1 - mu2 = 0 Ha: mu1 - mu2 not = 0 Without calculating the two-sample t statistic, would you reject the null hypothesis of equal population means at the 5% level of significance? Explain your answer.

   • (c) Complete the test of hypothesis from part (b). Do your decision and conclusion agree with what you found in part (b)?