Counselors at a summer camp for overweight and obese adolescents develop a weight-management program for each...
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Counselors at a summer camp for overweight and obese adolescents develop a weight-management program for each camper that centers on nutrition education and physical activity. In a recent study the body mass index (BMI) was measured for each of 74 campers both at the start and end of camp. Summary statistics on BMI measurements are shown in the table to the right. Complete parts a through h a. Give the null and alternative hypotheses for determining whether the mean BM at the end of camp is less than the mean BMI at the start of camp Let be the population mean BMI at the start of camp. 2 be the population mean BM at the end of camp, and 42: Mo b. How should the data be analyzed, as an independent-samples t-test or as a paired-difference t-test? Explain Choose the corect answer below OA. Use a paired-difference t-test because the assumption of independent samples is invalid ⒸB.Use an independent samples 1-dest because the sample of differences was chosen randomly OC. Use an independent samples 1-test because the sample size is greater than 30. By the Central Limit Theorem, this condition guarantees the test statistic will be approximately normal. OD. Use a paired difference 1-dest because, although the data were not paired originally pairing them after samping significantly reduces variation within the samples e. Calculate the test statistic using the formula for an independent-samples t-test Round to two decimal places as needed) d. Calculate the test statstic using the formula for paired-difference 1-st 1(Round to two decimal places as needed.) e. Compare the test statistics, parts and d. Which test statistic provides more evidence in support of the alternative hypothesis? A. The test statistic using the formula for paired-difference-test OB. The test statistic using the formula for an independent samples-test f. The p-value of the test, part d, was reported as p<0.0001. Interpret this result assuming -0.01. Ho because the p-value is the significance level. There is g. Do the differences in BMI values need to be normally distributed in order for the inference, part f, to be valid? Explain Choose the correct answer below A. No, as long as the distribution of each sample is approximately normal, the differences do not need to be ⒸB. No: the sample size is large enough that the Central Limit Theorem applies ⒸG. Yes, the differences must be normally distributed because the data are paired ⒸD. Yes, in order to make valid smal-sample inferences about the differences need to be normally distributed evidence that the mean BM at the end of camp is the mean BMI at the start of camp Standard MeanDeviation 33.9 5.8 Ending 30.3 5.2 BMI Paired Differences 3.6 Starting BMI 1.7 h. Find a 99% confidence interval for the true mean change in BMI for the campers The 99% confidence interval is (Round to three decimal places as needed.) interpret the result The true mean difference between the BMI at the start of camp and the BMI at the end of camp fails BMI at the end of camp is the mean BMI at the start of comp the limits of the interval, with confidence. Since 0 included in the interval, there is evidence that the mean Counselors at a summer camp for overweight and obese adolescents develop a weight-management program for each camper that centers on nutrition education and physical activity. In a recent study the body mass index (BMI) was measured for each of 74 campers both at the start and end of camp. Summary statistics on BMI measurements are shown in the table to the right. Complete parts a through h a. Give the null and alternative hypotheses for determining whether the mean BM at the end of camp is less than the mean BMI at the start of camp Let be the population mean BMI at the start of camp. 2 be the population mean BM at the end of camp, and 42: Mo b. How should the data be analyzed, as an independent-samples t-test or as a paired-difference t-test? Explain Choose the corect answer below OA. Use a paired-difference t-test because the assumption of independent samples is invalid ⒸB.Use an independent samples 1-dest because the sample of differences was chosen randomly OC. Use an independent samples 1-test because the sample size is greater than 30. By the Central Limit Theorem, this condition guarantees the test statistic will be approximately normal. OD. Use a paired difference 1-dest because, although the data were not paired originally pairing them after samping significantly reduces variation within the samples e. Calculate the test statistic using the formula for an independent-samples t-test Round to two decimal places as needed) d. Calculate the test statstic using the formula for paired-difference 1-st 1(Round to two decimal places as needed.) e. Compare the test statistics, parts and d. Which test statistic provides more evidence in support of the alternative hypothesis? A. The test statistic using the formula for paired-difference-test OB. The test statistic using the formula for an independent samples-test f. The p-value of the test, part d, was reported as p<0.0001. Interpret this result assuming -0.01. Ho because the p-value is the significance level. There is g. Do the differences in BMI values need to be normally distributed in order for the inference, part f, to be valid? Explain Choose the correct answer below A. No, as long as the distribution of each sample is approximately normal, the differences do not need to be ⒸB. No: the sample size is large enough that the Central Limit Theorem applies ⒸG. Yes, the differences must be normally distributed because the data are paired ⒸD. Yes, in order to make valid smal-sample inferences about the differences need to be normally distributed evidence that the mean BM at the end of camp is the mean BMI at the start of camp Standard MeanDeviation 33.9 5.8 Ending 30.3 5.2 BMI Paired Differences 3.6 Starting BMI 1.7 h. Find a 99% confidence interval for the true mean change in BMI for the campers The 99% confidence interval is (Round to three decimal places as needed.) interpret the result The true mean difference between the BMI at the start of camp and the BMI at the end of camp fails BMI at the end of camp is the mean BMI at the start of comp the limits of the interval, with confidence. Since 0 included in the interval, there is evidence that the mean
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SOLUTION Answer a Let Mi be the mean BPMI at the start of camp and M mean BMI at the end of Camp ... View the full answer
Related Book For
Statistics for Business and Economics
ISBN: 978-0321826237
12th edition
Authors: James T. McClave, P. George Benson, Terry T Sincich
Posted Date:
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