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). Given below are the BMI statistics for random samples of males and females from Data Set 1 in Appendix B. Use a 0.05 significance level to test the claim that males and females have the same mean BMI.

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. Do the following:
a. Test the given claim using the P-value method or critical value method.
b. Construct a confidence interval suitable for testing the given claim.

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Male BMI n = 40, x= 28.44075, s = 7.394076 Female BMI π = 40, x = 26.6005, s = 5.359442