10.2B Homework
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1. Under what conditions should you use a paired t procedure?
2. In a matched pairs t procedure, what is μ, the parameter of interest?
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3. What is the difference in the purposes for randomly selecting and randomly assigning?
4. What does it mean if an inference procedure is robust?
5. If the size of the SRS is less than 15, when can we use t procedures on the data?
6. If the size of the SRS is at least 15, when can we use t procedures on the data?
7. If the size of the SRS is at least 30, when can we use t procedures on the data?
8. Do piano lessons improve the spatial-temporal reasoning of preschool children?
Neurobiological arguments suggest that this may be true. A study designed to test this
hypothesis measured spatial-temporal reasoning of 34 preschool children before and after six
months of piano lessons. (The study also included children who took computer lessons and a
control group; but we are not concerned with those here.) The changes in the reasoning scores
are
2
3
3
5
4
4
7
9
6
-2
4
7
2
5
-2
7
2
7
4
9
-3
(a) Display the data and summarize the distribution.
1
6
3
0
0
4
7
3
4
3
6
4
-1
(b) Construct and interpret a 95% confidence interval for the mean improvement in
reasoning scores.
(c) Can we conclude that playing the piano causes an improvement in spatial-temporal
reasoning in children? Justify your answer.
9. Turn to page 651 in your book and look at example 10.10.
(a) This study was double-blind? What does this mean?
(b) Examine the differences in beats per minute with and without caffeine with graphs and
numerical summaries. Write a few sentences describing what you see.
(c) Is it appropriate to use t-procedures to construct a 90% confidence interval for the mean
difference in heart beats per minute? If so, do it. If not, explain why not.
10. In each of the following situations, discuss whether it would be appropriate to construct a tinterval to estimate the population mean.
(a) We want to estimate the average age at which U.S. presidents have died. So we obtain a
list of all U.S. presidents who have died and their ages at death.
(b) How much time do students spend on the internet? We collect data from the 32
members of an AP Statistics class and calculate the mean amount of time that each
student spent on the internet yesterday.
(c) The stemplot below shows the force required to pull apart 20 pieces of Douglas fir.