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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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  1. 28 September, 09:57
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    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
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