Question

# According to a study published in the New England Journal of Medicine, overweight people on low-carbohydrate...

According to a study published in the New England Journal of Medicine, overweight people on low-carbohydrate and Mediterranean diets lost more weight and got greater cardiovascular benefits than people on a conventional low-fat diet (The Boston Globe, July 17, 2008). A nutritionist wishes to verify these results and documents the weight loss (in pounds) of 30 dieters on the low-carbohydrate and Mediterranean diets and 30 dieters on the low-fat diet. Let Low-carb or Mediterranean and Low-fat diets represent populations 1 and 2, respectively. (You may find it useful to reference the appropriate table: z table or t table)

 Low-carb/ Mediterranean Diets Low-fat Diet Low-carb/ Mediterranean Diets Low-fat Diet 9.5 6.5 6.8 5.9 8.1 5.8 9.1 6.9 10.4 9.9 9.4 9.1 11.9 5.1 10.2 8.0 11.8 8.0 9.5 8.9 12.6 6.3 9.5 3.4 6.7 6.3 9.4 4.6 9.6 4.4 12.0 6.2 11.6 5.7 9.9 4.6 8.4 5.9 9.7 6.7 9.0 6.8 9.2 4.6 7.5 5.1 13.0 7.1 7.2 6.3 11.3 11.0 8.5 5.5 13.6 4.5 8.8 5.5 9.0 3.9

a. Set up the hypotheses to test the claim that the mean weight loss for those on low-carbohydrate or Mediterranean diets is greater than the mean weight loss for those on a conventional low-fat diet.

• H0: μ1μ2 = 0; HA: μ1μ2 ≠ 0

• H0: μ1μ2 ≥ 0; HA: μ1μ2 < 0

• H0: μ1μ2 ≤ 0; HA: μ1μ2 > 0

b-1. Calculate the value of the test statistic. Assume that the population variances are unknown but equal. (Round your answer to 3 decimal places.)

b-1. Find the p-value

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

c. At the 5% significance level, can the nutritionist conclude that people on low-carbohydrate or Mediterranean diets lose more weight than people on a conventional low-fat diet?

• Yes

• No

a) H0: μ1 − μ2 ≤ 0; HA: μ1 − μ2 > 0

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b-1) t = 7.581

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p-value < 0.01

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c) Yes, because p-value < 0.05 so, we Reject the null hypothesis

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I have used Excel and the command

Data > Data Analysis > T -test with equal variances > select the data > ok

below is the output

 t-Test: Two-Sample Assuming Equal Variances Variable 1 Variable 2 Mean 9.773333 6.283333333 Variance 3.197885 3.160747126 Observations 30 30 Pooled Variance 3.179316 Hypothesized Mean Difference 0 df 58 t Stat 7.581 P(T<=t) one-tail 1.55E-10 t Critical one-tail 1.671553 P(T<=t) two-tail 3.1E-10 t Critical two-tail 2.001717

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