Question

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.

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: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 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-2. 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, on average, than people on a conventional low-fat diet?

• Yes

• No

Answer 1