A six-week fitness program was designed to decrease the time it takes retired individuals to walk one mile. At the beginning of the program, 20 randomly selected retired individuals were invited to participate, and their times to walk a mile were recorded. After the six-week program, their times to walk a mile were again recorded. Most participants saw little to no improvement in their times to walk one mile; however, a few participants saw drastic improvements in their times to walk one mile. The program director would like to perform a hypothesis test to determine if the program reduces the mean time for retired individuals to walk a mile. Which of the following statements is true? (A) Because there are 40 observations in total, the sample size is large enough to assume that the sampling distribution of the sample mean differences is approximately normal. (B) (C) Because the walk times before and after the program are paired, a hypothesis test is not appropriate. The sampling distribution of sample means can be assumed to be approximately normal because the distribution of the sample data is not skewed. (D) Because the sample size of 20 is less than 30 and the improvements in walk times in the sample data appear to be skewed, the distribution of sample means should not be assumed to be approximately normal. (E) Because the program recruited only retired individuals, the distribution of sample means should not be assumed to be approximately normal.
A six-week fitness program was designed to decrease the time it takes retired individuals to walk one mile. At the beginning of the program, 20 randomly selected retired individuals were invited to participate, and their times to walk a mile were recorded. After the six-week program, their times to walk a mile were again recorded. Most participants saw little to no improvement in their times to walk one mile; however, a few participants saw drastic improvements in their times to walk one mile. The program director would like to perform a hypothesis test to determine if the program reduces the mean time for retired individuals to walk a mile. Which of the following statements is true? (A) Because there are 40 observations in total, the sample size is large enough to assume that the sampling distribution of the sample mean differences is approximately normal. (B) (C) Because the walk times before and after the program are paired, a hypothesis test is not appropriate. The sampling distribution of sample means can be assumed to be approximately normal because the distribution of the sample data is not skewed. (D) Because the sample size of 20 is less than 30 and the improvements in walk times in the sample data appear to be skewed, the distribution of sample means should not be assumed to be approximately normal. (E) Because the program recruited only retired individuals, the distribution of sample means should not be assumed to be approximately normal.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 27PPS
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Question
Why is it that the correct answer is D? How can we know that the data appear to be skewed in the given problem? What are the hint words in the situation that we can say it is skewed?
Transcribed Image Text:A six-week fitness program was designed to decrease the time it takes retired individuals to walk one mile. At the
beginning of the program, 20 randomly selected retired individuals were invited to participate, and their times to
walk a mile were recorded. After the six-week program, their times to walk a mile were again recorded. Most
participants saw little to no improvement in their times to walk one mile; however, a few participants saw drastic
improvements in their times to walk one mile. The program director would like to perform a hypothesis test to
determine if the program reduces the mean time for retired individuals to walk a mile.
Which of the following statements is true?
(A)
Because there are 40 observations in total, the sample size is large enough to assume that the sampling
distribution of the sample mean differences is approximately normal.
(B)
(C)
Because the walk times before and after the program are paired, a hypothesis test is not appropriate.
The sampling distribution of sample means can be assumed to be approximately normal because the
distribution of the sample data is not skewed.
(D)
Because the sample size of 20 is less than 30 and the improvements in walk times in the sample data appear
to be skewed, the distribution of sample means should not be assumed to be approximately normal.
(E)
Because the program recruited only retired individuals, the distribution of sample means should not be
assumed to be approximately normal.
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