Jillian Michaels and Bob Harper are all- time famous American trainers. Michaels thinks that her clients lose more weight on average than the clients of Harper. Harper naturally disagrees with Michaels. In order to settle the dispute, the two trainers agree to each work with 15 different clients for six months. The table below summarizes the weight loss (Ibs) of each group: J. Michaels Harper Mean 25 21 SD 5.1 2.5 Size 15 15 1. Assume normality in the population distribution, construct a 90% confidence interval for the population difference of the mean weight loss using the critical value of 1.76 (Note: all values are given, no R codes needed) 2. What does it mean to be at "90% confident"? Would the 95% confidence interval be wider or narrower? Would the margin of error be wider or narrower? (Note: no calculation is needed) 3. According to the confidence interval you found in part (a), what can be concluded about Michaels' claim? (Note: you do NOT need to do the 5-step significance test here, just answer the B.

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Author:Amos Gilat
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Jillian Michaels and Bob Harper are all-
time famous American trainers. Michaels
thinks that her clients lose more weight on
average than the clients of Harper. Harper
naturally disagrees with Michaels. In order
to settle the dispute, the two trainers
agree to each work with 15 different
clients for six months. The table below
summarizes the weight loss (Ibs) of each
group:
J.
В.
Michaels Harper
Mean
25
21
SD
5.1
2.5
Size
15
15
1. Assume normality in the population
distribution, construct a 90%
confidence interval for the population
difference of the mean weight loss
using the critical value of 1.76 (Note: all
values are given, no R codes needed)
2. What does it mean to be at "90%
confident"? Would the 95% confidence
interval be wider or narrower? Would
the margin of error be wider or
narrower? (Note: no calculation is
needed)
3. According to the confidence interval
you found in part (a), what can be
concluded about Michaels' claim?
(Note: you do NOT need to do the 5-step
significance test here, just answer the
question and explain in a sentence)
Transcribed Image Text:Jillian Michaels and Bob Harper are all- time famous American trainers. Michaels thinks that her clients lose more weight on average than the clients of Harper. Harper naturally disagrees with Michaels. In order to settle the dispute, the two trainers agree to each work with 15 different clients for six months. The table below summarizes the weight loss (Ibs) of each group: J. В. Michaels Harper Mean 25 21 SD 5.1 2.5 Size 15 15 1. Assume normality in the population distribution, construct a 90% confidence interval for the population difference of the mean weight loss using the critical value of 1.76 (Note: all values are given, no R codes needed) 2. What does it mean to be at "90% confident"? Would the 95% confidence interval be wider or narrower? Would the margin of error be wider or narrower? (Note: no calculation is needed) 3. According to the confidence interval you found in part (a), what can be concluded about Michaels' claim? (Note: you do NOT need to do the 5-step significance test here, just answer the question and explain in a sentence)
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