The Paleo diet allows only for foods that humans typically consumed over the last 2.5 million years, excluding those agriculture-type foods that arose during the last 10,000 years or so. Researchers randomly divided 500 volunteers into two equal-sized groups. One group spent 6 months on the Paleo diet. The other group received a pamphlet about controlling portion sizes. At the beginning of the study, the difference in mean weight between the two groups was approximately equal to 0. After the study, the Paleo group had lost on average of 7 pounds with a standard deviation of 20 pounds while the control group had lost on average of 5 pounds with a standard deviation of 12 pounds. (a) Create a 95% confidence interval for the difference in mean weight loss for the two groups (Paleo minus Control). For degrees of freedom, use Min(N1-1,N2-1), and for the corresponding t* use either Table D (with degrees of freedom closest to the exact value) or Excel. Give your answer to 3 decimal places

Lower Bound:

Upper Bound:

The confidence interval in which the difference in the weight lost by the two group lies using a confidence level of 95% is (0.891 ; 4.891)

The confidence interval for the mean difference is defined thus :

Mean difference ± S.E

degree of freedom, df = n1 + n2 - 2 = (500 - 2) = 498

Critical level = t* at df = 498 = ±1.96

Mean difference = (μ1 - μ2) = 7 - 5 = 2

Standard Error = [tex]t* \times \sqrt{\frac{s_{1}}^{2}{n_1} + \frac{s_{2}}^{2}{n_2}} = \sqrt{\frac{20^{2}}{250} + \frac{12^{2}}{250}} = 1.96 \times 1.475 = 2.891 [/tex]

Lower boundary = 2 - 2.891 = 0.891

Upper boundary = 2 + 2.891 = 4.891

Therefore, the confidence interval is (0.891 ; 4.891)

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