Question

8. We know that the mean weight of men is greater than the mean weight of women, and the mean height of men is greater than the mean height of women. A person’s body mass index (BMI) is computed by dividing weight (kg) by the square of height (m). Use α = 0.05 significance level to test the claim that females and males have the same mean BMI. Below are the statistics for random samples of females and males. Female BMI: n = 75, ?̅= 29.04, s = 7.32 Male BMI: n = 85, ?̅= 28.33, s = 5.31

(a) identify the claim and state H0 and H1

(b) find the critical value

(c) find the test statistic

(d) decide whether to reject or fail to reject the null hypothesis

(e) interpret the decision in the context of the original claim.

Answer 1

A)Claim is that BMI for men and women are the same

H₀ : There is no significant difference in the mean BMI of men and women (ie)

H₁ : There is significant difference in the mean BMI of men and women (ie)

B)Critical value is t_.05,158 = 1.975

C)Test statistic is

The value is .708

D)Since t < t_cric , we accept the null hypothesis.

E)The claim is true that male and female have the same BMI