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Summer weight-loss camp. Camp Jump Start is an 8-week
Chapter 8, Problem 31E(choose chapter or problem)
Problem 31E
Summer weight-loss camp. Camp Jump Start is an 8-week summer camp for overweight and obese adolescents. Counselors develop a weight-management program for each camper that centers on nutrition education and physical activity. In a study published in Pediatrics (April 2010), the body mass index (BMI) was measured for each of 76 campers both at the start and end of camp. Summary statistics on BMI measurements are shown in the table.
|
Mean |
Standard Deviation |
|
Starting BMI Ending BMI Paired Differences |
34.9 31.6 3.3 |
6.9 6.2 1.5 |
a. Give the null and alternative hypothesis for determining whether the mean BMI at the end of camp is less than the mean BMI at the start of camp.
b. How should the data be analyzed, as an independent- samples t -test or as a paired-difference t -test? Explain.
c. Calculate the test statistic using the formula for an independent-samples t-test. ( Note : This is not how the test should be conducted.)
d. Calculate the test statistic using the formula for a paired-difference t -test.
e. Compare the test statistics, parts c and d . Which test statistic provides more evidence in support of the alternative hypothesis?
f. The p -value of the test, part d , was reported as p<6 .0001. Interpret this result assuming α = .01 .
g. Do the differences in BMI values need to be normally distributed in order for the inference, part f , to be valid? Explain.
h. Find a 99% confidence interval for the true mean change in BMI for Camp Jump Start campers. Interpret the result.
Questions & Answers
QUESTION:
Problem 31E
Summer weight-loss camp. Camp Jump Start is an 8-week summer camp for overweight and obese adolescents. Counselors develop a weight-management program for each camper that centers on nutrition education and physical activity. In a study published in Pediatrics (April 2010), the body mass index (BMI) was measured for each of 76 campers both at the start and end of camp. Summary statistics on BMI measurements are shown in the table.
|
Mean |
Standard Deviation |
|
Starting BMI Ending BMI Paired Differences |
34.9 31.6 3.3 |
6.9 6.2 1.5 |
a. Give the null and alternative hypothesis for determining whether the mean BMI at the end of camp is less than the mean BMI at the start of camp.
b. How should the data be analyzed, as an independent- samples t -test or as a paired-difference t -test? Explain.
c. Calculate the test statistic using the formula for an independent-samples t-test. ( Note : This is not how the test should be conducted.)
d. Calculate the test statistic using the formula for a paired-difference t -test.
e. Compare the test statistics, parts c and d . Which test statistic provides more evidence in support of the alternative hypothesis?
f. The p -value of the test, part d , was reported as p<6 .0001. Interpret this result assuming α = .01 .
g. Do the differences in BMI values need to be normally distributed in order for the inference, part f , to be valid? Explain.
h. Find a 99% confidence interval for the true mean change in BMI for Camp Jump Start campers. Interpret the result.
ANSWER:Solution
Step 1 of 8
a) We have to write the null and alternative hypothesis
Here the claim is that the mean BMI at the end of the camp is less than the mean BMI at the start of the camp
Let is the mean of the starting BMI
And is the mean of the ending BMI
ThenThe mean BMI at the end of the camp is same as
the mean BMI at the start of the camp
(
And The mean BMI at the end of the camp is same as
the mean BMI at the start of the camp