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	50	50
x̄	27.7419	26.4352
s	8.437128	5.693359

a) Test the claim that males and females have the same mean body mass index. What are the null and alternative hypotheses?

What is the test statistic?

What is the p-value?

State the conclusion for this test.

b) Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI.

Does the confidence interval support the conclusion of the test?

Answer 1

using minitab>stat>basic stat>two sample t test we have

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 50 27.74 8.44 1.2
2 50 26.44 5.69 0.81

Difference = μ (1) - μ (2)
Estimate for difference: 1.31
99% CI for difference: (-2.49, 5.10)
T-Test of difference = 0 (vs ≠): T-Value = 0.91 P-Value = 0.367 DF = 85

a) we have given

claim: males and females have the same mean body mass index.

the null and alternative hypotheses are

the test statistic t = 0.91

the p-value =0.367

\conclusion: since p-value is greater than 0.01 so do not reject H0, we have sufficient evidence to accept the claim

b) the 99% confidence interval is (-2.49, 5.10)

yes the confidence interval support the conclusion of the test because the confidence interval contains 0