Question

given in the table are the bmi statistics for random samples of men and women. assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. complete parts (a) and (b) below. use a 0.01 significance level for both parts.

male bmi female bmi
μ μ₁ μ₂
n 40 40
x̄ 27.0039 24.1173
s 7.101911 4.141761

a. test the claim that males and females have the same mean body mass index (bmi).
what are the null and alternative hypotheses?
a. h₀: μ₁ ≥ μ₂
h₁: μ₁ < μ₂
b. h₀: μ₁ = μ₂
h₁: μ₁ > μ₂
c. h₀: μ₁ ≠ μ₂
h₁: μ₁ < μ₂
d. h₀: μ₁ = μ₂
h₁: μ₁ ≠ μ₂

Explanation:

When testing the claim that two populations have the same mean (in this case, males and females having the same mean BMI), the null hypothesis \(H_0\) assumes equality of the means (\(\mu_1=\mu_2\)). The alternative hypothesis \(H_1\) for a two - tailed test (since we are just testing if they are not equal, not specifically greater or less) is \(\mu_1
eq\mu_2\).

Answer:

D. \(H_0:\mu_1 = \mu_2\), \(H_1:\mu_1
eq\mu_2\)