A group of 78 people enrolled in a weight-loss program that involved adhering to a special diet and to exercise daily. After six months, their mean weight loss was 25 pounds with a sample standard deviation of 9 pounds. The second group of 43 people went on the same diet but did not exercise. After six months, their mean weight loss was 14 pounds with a standard deviation of 7 pounds.

Find a 95% confidence interval for the mean difference between the weight losses.

Question

Mathematics

Bruno Kirby

28 September, 09:29

A group of 78 people enrolled in a weight-loss program that involved adhering to a special diet and to exercise daily. After six months, their mean weight loss was 25 pounds with a sample standard deviation of 9 pounds. The second group of 43 people went on the same diet but did not exercise. After six months, their mean weight loss was 14 pounds with a standard deviation of 7 pounds.

Find a 95% confidence interval for the mean difference between the weight losses.

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Answers (1)

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Iliana Conley · Answer 1

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

z = (x1 - x2) ± √ (s²/n1 + s2²/n2)

Where

x1 = sample mean of group 1

x2 = sample mean of group 2

s1 = sample standard deviation for data 1

s2 = sample standard deviation for data 2

For a 95% confidence interval, the z score is 1.96

From the information given,

x1 = 25 pounds

s1 = 9 pounds

n1 = 78

x2 = 14 pounds

s2 = 7 pounds

n2 = 43

x1 - x2 = 25 - 14 = 11

√ (s²/n1 + s2²/n2) = √ (9²/78 + 7²/43) = √1.038 + 1.1395)

= 1.48

The upper boundary for the confidence interval is

11 + 1.48 = 12.48 pounds

The lower boundary for the confidence interval is

11 - 1.48 = 9.52 pounds