Question

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.

Answer 1

To find a 95% confidence interval for the mean difference between the weight losses of the two groups, we can use the formula: CI = (X1 - X2) ± Z * sqrt((s1^2 / n1) + (s2^2 / n2)). Plugging in the values from the question and simplifying the calculation, we find that the 95% confidence interval is (8.7818, 13.2182) pounds.

Step-by-step explanation:

To find a 95% confidence interval for the mean difference between the weight losses of the two groups, we can use the formula:

CI = (X1 - X2) ± Z * sqrt((s1^2 / n1) + (s2^2 / n2))

Where:

• X1 is the mean weight loss of the first group
• X2 is the mean weight loss of the second group
• s1 is the sample standard deviation of the first group
• s2 is the sample standard deviation of the second group
• n1 is the sample size of the first group
• n2 is the sample size of the second group
• Z is the critical value for a 95% confidence level (which is approximately 1.96)

Plugging in the values from the question:

X1 = 25 pounds, X2 = 14 pounds, s1 = 9 pounds, s2 = 7 pounds, n1 = 78, n2 = 43

Let's calculate the confidence interval:

CI = (25 - 14) ± 1.96 * sqrt((9^2 / 78) + (7^2 / 43))

CI = 11 ± 1.96 * sqrt(0.9259 + 0.3588)

CI = 11 ± 1.96 * sqrt(1.2847)

CI = 11 ± 1.96 * 1.1334

CI = 11 ± 2.2182

The 95% confidence interval for the mean difference between the weight losses is (8.7818, 13.2182) pounds.