9) please help Given in the table are the BMI statistics for random samples of m

Question

9) please help

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. 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. 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. 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 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.

Explanation / Answer

Below are the null and alternate hypothesis
H0: mu1 = mu2
H1: mu1 not equals to mu2

test statistics, t = 1.0863

p-value = 0.2809

As p-value is greater than significance level, we fail to reject the null hypothesis. Hence option (B)

(B)

lets consider CI = 95% and respective t-value = 1.99

lower limit = (x1bar - x2bar) - t*SE = 1.3998 - 1.99*1.29 = -1.169

upper limit = (x1bar - x2bar) + t*SE = 1.3998 + 1.99*1.29= 3.9686

Hence, -1.169 < mu1-mu2 < 3.9686

x1(bar) 27.0811 x2(bar) 25.6813 s1 8.167378 s2 4.040129 n1 50 n2 50 SE = sqrt[ (s12/n1) + (s22/n2) ] (s12/n1) 1.3341 (s22/n2) 0.3265 SE 1.29 DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] } [ (s12 / n1)2 / (n1 - 1) ] 0.036324 [ (s22 / n2)2 / (n2 - 1) ] 0.002175 (s12/n1 + s22/n2)2 2.757506 DF = 72

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