1. The effectiveness of two methods of teaching statistics is compared. A class of 20 stu- dents is randomly divided into 2 groups and each group is taught according to a different method. The test scores of the two groups at the end of the semester show the following characteristics: Group 1: ₁9 = = 74.5 s² = 94.6 =71.8 s = 102.6 Group 2: n₂ = 11 Round all calculations (including intermediate calculations) to 3 decimals. (a) Assuming underlying independent normal distributions with = o, find a 96% confidence interval for ₁-₂. (b) Does there appear to be a difference in teaching methods, based on the confidence interval you found in Question la? Why or why not? (c) (Graduate Student Only) Use the setup from Question 1 to answer the following questions. i. Compute a 90% confidence interval for o/o2, the ratio of the population vari- ances. Round values to 3 decimals. ii. Do we have a reason to believe that of and o2 are equal, based on the confidence interval you found in Question 1(c)i? Why or why not?

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1. The effectiveness of two methods of teaching statistics is compared. A class of 20 stu-
dents is randomly divided into 2 groups and each group is taught according to a different
method. The test scores of the two groups at the end of the semester show the following
characteristics:
Group 1: ₁9
=
= 74.5 s² = 94.6
=71.8 s = 102.6
Group 2: n₂ = 11
Round all calculations (including intermediate calculations) to 3 decimals.
(a) Assuming underlying independent normal distributions with = o, find a 96%
confidence interval for ₁-₂.
(b) Does there appear to be a difference in teaching methods, based on the confidence
interval you found in Question la? Why or why not?
(c) (Graduate Student Only) Use the setup from Question 1 to answer the following
questions.
i. Compute a 90% confidence interval for o/o2, the ratio of the population vari-
ances. Round values to 3 decimals.
ii. Do we have a reason to believe that of and o2 are equal, based on the confidence
interval you found in Question 1(c)i? Why or why not?
Transcribed Image Text:1. The effectiveness of two methods of teaching statistics is compared. A class of 20 stu- dents is randomly divided into 2 groups and each group is taught according to a different method. The test scores of the two groups at the end of the semester show the following characteristics: Group 1: ₁9 = = 74.5 s² = 94.6 =71.8 s = 102.6 Group 2: n₂ = 11 Round all calculations (including intermediate calculations) to 3 decimals. (a) Assuming underlying independent normal distributions with = o, find a 96% confidence interval for ₁-₂. (b) Does there appear to be a difference in teaching methods, based on the confidence interval you found in Question la? Why or why not? (c) (Graduate Student Only) Use the setup from Question 1 to answer the following questions. i. Compute a 90% confidence interval for o/o2, the ratio of the population vari- ances. Round values to 3 decimals. ii. Do we have a reason to believe that of and o2 are equal, based on the confidence interval you found in Question 1(c)i? Why or why not?
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