The accompanying table gives results from a study of the words spoken in a day by men and women, and the original data are in Data Set 17 in Appendix B. Use a 0.01 significance level to test the claim that the mean number of words spoken in a day by men is less than that for 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. 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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Men n, = 186 저 = 15,668.5 = 16,215.0 s, = 8632.5 82-7301.2 Women n2 = 210