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. the test statistic, t, is 2.22. (round to two decimal places as needed.) the p - value is 0.029. (round to three decimal places as needed.) state the conclusion for the test. a. fail to reject the null hypothesis. there is not sufficient evidence to warrant rejection of the claim that men and women have the same mean bmi. b. reject the null hypothesis. there is not sufficient evidence to warrant rejection of the claim that men and women have the same mean bmi. c. fail to reject the null hypothesis. there is sufficient evidence to warrant rejection of the claim that men and women have the same mean bmi. d. reject the null hypothesis. there is sufficient evidence to warrant rejection of the claim that men and women have the same mean bmi.

Explanation:

To decide whether to reject the null hypothesis, we compare the P - value with the significance level. The significance level \(\alpha = 0.01\). If \(P-\text{value}\leq\alpha\), we reject the null hypothesis; if \(P - \text{value}>\alpha\), we fail to reject the null hypothesis. Here, \(P-\text{value}=0.029\) and \(\alpha = 0.01\). Since \(0.029>0.01\) (i.e., \(P-\text{value}>\alpha\)), we fail to reject the null hypothesis. When we fail to reject the null hypothesis, it means there is not sufficient evidence to warrant rejection of the claim (in this case, the claim that men and women have the same mean BMI).

Answer:

A. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.