In: Statistics and Probability
Researchers studied the effects of adding an exercise program to
dieting in the achievement of weight loss. A sample of
96 men ages 18-20 (Group 1) were observed for
weight loss using a diet only, and another independent sample of
46 men ages 18-20 (Group 2) were put on the same
diet, but with an added exercise program. The mean weight loss for
Group 1 was 8.9 pounds with a standard deviation of 4.1 pounds, and
the mean weight loss for Group 2 was 15.3 pounds, with a standard
deviation of 6.1 pounds.
Calculate the lower bound of a 95% confidence
interval for the difference in mean weight loss for the
two groups to two decimal places. Assume the population standard
deviations are NOT equal (Case 2). For the degrees
of freedom value, v, for the Student's t
distribution that you need to make the interval, use this website
http://web.utk.edu/~cwiek/TwoSampleDoF
Take all calculations toward the answer to three (3) decimal places.
, ,
, ,
The confidence interval is given by
The confidence interval is given by
tcritical, for = 0.05(for 2 tails) , degrees of freedom = n2-1(smaller of the 2) = 46-1 = 45 is 2.014(Taken to 3 decimal places as required)
taken to 3 decimal places as required.
The Lower Limit = -6.40 - 2.014 * 0.992 = -8.39789 -8.40 (Rounded to 2 decimal places)
The Upper Limit = -6.40 + 2.014 * 0.992 = -4.40211 -4.40 (Rounded to 2 decimal places)
Therefore,
The lower bound of the confidence interval is -8.40.
The Upper bound of the confidence interval is -4.40.