A study was done on body temperatures of men and women. The results are shown in

Question

A study was done on body temperatures of men and women. The results are shown in the table. 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 0.05 significance level for both parts. The test statistic, t, is 0.58. (Round to two decimal places as needed.) The P-value is 0.282. (Round to three decimal places as needed.) State the conclusion for the test. Reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women. Reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.

Explanation / Answer

Ans: Option C is correct.below is explanation for the same.

t=(97.55-97.39)/sqrt((0.862/11)+(0.732/59))=0.58

For above question t score=0.58

For degree of freedom df=11-1=10,(In this case,where population standard deviations are not same,the conservative option to using the exact degrees of freedom calculation can be made by choosing the smaller of n11 and n21)

P(T<t)=0.71268(left-tailed p-value for t=0.58 and df=68)

But we need right tail p-value=1-0.7126=0.2874 or 0.29

Now p-value=0.29>0.05,hence,we fail to reject the null hypothesis or we accept the null hypthesis and reject the alternate hypotheis that men have higher mean body temperature than women.

So answer will be option C,that says we fail to reject null hypotheis and there is not sufficient evidence that men have higher body temperature than women.

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