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. To justify the cost of the camp, counselors must provide empirical evidence that the weight-management program is effective. 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.

a. Give the null and alternative hypotheses 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 test or as a paired difference test? Explain.
c. Calculate the test statistic using the formula for an independent samples test. (This is not how the test should be conducted.)
d. Calculate the test statistic using the formula for a paired difference 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 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.

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Mean Standard Deviation Starting BMI Ending BMI Paired Differences 34.9 31.6 3.3 6.9 6.2 L.5