Question

A regort included the fallowing information an the heights (in.) for non-Hispanic white females. Sample Sample Std. Error Age Size Mean Mean 20-39 869 6 3,6 0,09 60 and older 938 61.8 0.11 (a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use #20-30-50 and older Interpret the interval. We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval. We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval. We cannot draw a conclusion from the given information. We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval (b) Let 4, derrote the population mean theight for those aged 20-39 and u, denate the population mean height for those aged 60 and older. Interpret the hypotheses Ho: 4, - = 1 and 2:4,-4 > 1. The null hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is 1 inch higher than for younger women. The null hypothesis states that the true mean height for older women is 1 inch higher than for younger worden. The alternative hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. The null hypothesis states that the true mean height for younger women is 1 inch higher than for alder woman. The alternative hypothesis states that the true mean height for younger women is more than 1 inch higher than for alder women. The null hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is 1 inch higher than for older women. Carry out a test of these hypotheses at significance level 0.001. Calculate the test statistic and determine the P value. (Round your test statistic ta tao dedmal places and your P-value to four decimal places.) P-value- (c) Based on the P-value calculated in (b) would you reject the null hypothesis at any reasonable significance level? Explain your reasoning. Reject Hy. The data does not suggest that the difference in the true average heights exceeds 1. Fail to reject Ho. The data suggests that the difference in the true average heights exceeds 1. Reject H. The data suggests that the difference in the true average heights exceeds 1. Fail to reject . The data does not suggest that the difference in the true average heights exceeds 1. to the younger age group, and you wanted to see if there was compelling evidence for concluding that the population mean height for younger women exceeded that for older women by (d) What hypotheses would be appropriate if , referred to the older age group marc than 1 in.? MO: 42 - 42 = -1 1:41-42 -1 Holly - --1 :44 - -1 HO: 41 -2-1 H: 11-21 H: 4,- 2-1 M: 1-21

Answer 1

solution Given 420-39 = 63.9 "Go &older=61.8 SE20-39) =0.09 5 0.091869 0,- 2.6531 Se Gofolder) ² 0 2 = 0.11 69 -0.11 *938 - 3.3689 291-954-1-095-0-05 Early 20.05 = 1.96 95% CI for difference of mean a 938 - 6639-618) 1964 2.683°, 3.36392 = (1.821433, 2.378566) ») (1.8214, 2.3786) we are 95%. confident that the bowe querage height of younger women to greater than the that of older women by an amount within confidence interval option k is correct b) to the null hypothesis states that the towe mean height for younger women is ninch higher than four older women. The alternative hypotter's states that the top mean height for younges women is more than inch higher chan for older women option 'B' iscared..

Z. 3,-Xg ,19 63.9-648 2.65312, 3.36892 -14.77565 V 869 938 = 14.78 P-value - 000001 c) Reject Ho. The data suggests that the difference in the average heights exceeds 1 option 'c' is correct, d) Ho: M-M=1 HaiMalgal eption 'd' is correct
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