Question

A group of 78 people enrolled in a weight-loss program that involved adhering to a special diet and to a daily exercise program. After six months, their mean weight loss was 25 pounds, with a sample standard deviation of 9 pounds. A second group of 43 went on the special diet, but did not exercise. After six months, their mean weight loss was 14 pounds, with a sample standard deviation of 7 pounds. a. What function would be used to construct a confidence interval for the difference in weight loss between the exercisers and the non-exercisers? b. Construct a 97.5% confidence interval for the difference in weight loss between the exercisers and the non-exercisers. Round your answers to two decimal places.( C. Based on your confidence interval, on average, which program has a higher weight loss?

Answer 1

a) two sample t test

b)

Here, T1 = 25.000, 1 = 9.0000, n1 = 78, 12 = 14.000, S2 = 7.0000, n2 = 43 and associated degrees of freedom + df= = 106 高 + ni-1 n2-1 The Standard error is 81 7.002 SE= 9.002 V 78 + 1.476 + ni n2 43 The critical value is tcritical = t 1-0.975 ,106 =t0.0125,106 = 2.273687 2.274 The margin of error is 2 81 S2 9.002 7.002 9.002 ME=t 1-0.975 t 19975,106 * + to.013,106 * + = 2.274* + 7.002 43 = 3.355516 3.356 ni n2 V 78 43 78 a 97.5 percent confidence interval for the differnce in population means (Mi - H2 ) is 81 = či - 02+ + *ti-0.975 ,106 ni n2 = 21 - 22 + ME = (25.000 – 14.000) 3.355516 = 11.000 + 3.355516 = (7.644484, 14.355516) (7.64, 14.36)

c) group with exercise program, since lower bound of the confidence interval > 0