9.40 Summer weight-loss camp. Camp Jump Start is an 8-week summer camp for overweight and obese adoles- cents. Counselors develop a weight-management pro- ogram for each camper that centers on nutrition education and physical activity. In a study published in Pediatrics (Apr. 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 34.9 6.9 31.6 6.2 Paired Differences 3.3 1.5 Based on Huelsing, J., Kanafani, N., Mao, J., and White, N. H. "Camp Jump Start: Effects of a residential summer weight-loss camp for older children and adolescents." Pediatrics, Vol. 125, No. 4, Apr. 2010 (Table 3). 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 1-test. e. Compare the test statistics, parts e and d. Which test statistic provides more evidence in support of the alter- native hypothesis? f. The p-value of the test, part d, was reported as p<.0001. Interpret this result assuming a = .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.
9.40 Summer weight-loss camp. Camp Jump Start is an 8-week summer camp for overweight and obese adoles- cents. Counselors develop a weight-management pro- ogram for each camper that centers on nutrition education and physical activity. In a study published in Pediatrics (Apr. 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 34.9 6.9 31.6 6.2 Paired Differences 3.3 1.5 Based on Huelsing, J., Kanafani, N., Mao, J., and White, N. H. "Camp Jump Start: Effects of a residential summer weight-loss camp for older children and adolescents." Pediatrics, Vol. 125, No. 4, Apr. 2010 (Table 3). 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 1-test. e. Compare the test statistics, parts e and d. Which test statistic provides more evidence in support of the alter- native hypothesis? f. The p-value of the test, part d, was reported as p<.0001. Interpret this result assuming a = .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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Author:Carter
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Chapter4: Equations Of Linear Functions
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Transcribed Image Text:9.40 Summer weight-loss camp. Camp Jump Start is an
8-week summer camp for overweight and obese adoles-
cents. Counselors develop a weight-management pro-
ogram for each camper that centers on nutrition education
and physical activity. In a study published in Pediatrics
(Apr. 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
34.9
6.9
31.6
6.2
Paired Differences
3.3
1.5
Based on Huelsing, J., Kanafani, N., Mao, J., and White, N. H. "Camp
Jump Start: Effects of a residential summer weight-loss camp for older
children and adolescents." Pediatrics, Vol. 125, No. 4, Apr. 2010 (Table 3).
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 1-test.
e. Compare the test statistics, parts e and d. Which test
statistic provides more evidence in support of the alter-
native hypothesis?
f. The p-value of the test, part d, was reported as p<.0001.
Interpret this result assuming a = .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.
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