Question

# 7. Given in the table are the BMI statistics for random samples of men and women....

7. 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 0.05 significance level for both parts.

 Male BMI Female BMI µ µ1 µ2 N 48 48 xˉ 27.6431 26.5609 s 7.105107 4.438441

The test​ statistic, t, is ____

​(Round to two decimal places as​ needed.)

The​ P-value is ____

​(Round to three decimal places as​ needed.)

State the conclusion for the test.

A.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.

B.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.

C.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 not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

b. Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI.

____<µ1-µ2<___

​(Round to three decimal places as​ needed.)

Does the confidence interval support the conclusion of the​ test?

(Yes,No,) because the confidence interval contains (only negative values, zero, only positive values.)

The pooled estimate is ,

Hypothesis : VS

The test statistic is ,

P-value : ; From Excel "=TDIST(0.59,94,2)"

Decision : Here , P-value = 0.5566 > 0.05

Therefore , fail to reject Ho

Conclusion :

B.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. The 95% confidence interval suitable for testing the claim that males and females have the same mean BMI is ,

; From excel "=TINV(0.05,94)"

Yes , The confidence interval support the conclusion of the​ test ,  because the confidence interval contains zero.

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