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. (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

Click here for the Excel Data File

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-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

Answer 1

a) H₀: μ₁ − μ₂ ≤ 0; H_A: 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