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.

b. construct a confidence interval suitable for testing the claim that males and females have the same mean bmi.
-0.567 < μ₁ - μ₂ < 6.340
(round to three decimal places as needed.)
does the confidence interval support the conclusion of the test?
because the confidence interval contains

Explanation:

Step1: Analyze the confidence interval

The confidence interval for \(\mu_1-\mu_2\) is \(- 0.567<\mu_1 - \mu_2<6.340\).

Step2: Check if zero is in the interval

Since \(0\) is within the interval \(-0.567\) to \(6.340\), it means that we cannot reject the null hypothesis \(H_0:\mu_1=\mu_2\) at the corresponding significance level.

Answer:

Yes, because the confidence interval contains \(0\).