Question

# Find the test statistic for the t test and state the conclusion.  Are low-fat diets or low-carb...

Find the test statistic for the t test and state the conclusion.  Are low-fat diets or low-carb diets more effective for weight loss? A sample of 78 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 15.0 pounds with a sample standard deviation of 7.77 pounds. A second sample of 74 subjects went on a low-fat diet. Their sample mean weight loss was 16.3 with a standard deviation of 6.10. Can you conclude that the mean weight loss differed between the two diets? Use the α = 0.01 level.

i). State the appropriate null and alternate hypotheses.
ii). Compute the test statistic.
iii). How many degrees of freedom are there, using the simple method?
iv). Do you reject H0? State a conclusion.

 i) H0: μ1 = μ2 versus H1: μ1 ≠ μ2 ii) -1.150 iii) 73 iv) No. There is insufficient evidence to conclude that the mean weight losses differ. i) H0: μ1 = μ2 versus H1: μ1 ≠ μ2 ii) -0.897 iii) 74 iv) Yes. There appears to be a difference in the mean weight losses. i) H0: μ1 = μ2 versus H1: μ1 ≠ μ2 ii) -1.150 iii) 74 iv) No. There is insufficient evidence to conclude that the mean weight losses differ. i) H0: μ1 = μ2 versus H1: μ1 ≠ μ2 ii) -0.897 iii) 73 iv) Yes. There appears to be a difference in the mean weight losses.

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