A report included the following information on the heights (in.)for non-Hispanic white females.

Age	Sample Size	Sample Mean	Std. Error Mean
20–39	863	65.7	0.09
60and older	939	64.1	0.11

(a)

Calculate a confidence interval at confidence levelapproximately 95% for the difference between population mean heightfor the younger women and that for the older women. (Useμ_20–39 − μ_{60 and older}.),

We are 95% confident that the true average height of younger womenis greater than that of older women by an amount within theconfidence interval.We are 95% confident that the true averageheight of younger women is greater than that of older women by anamount outside the confidence interval.    Wecannot draw a conclusion from the given information.We are 95%confident that the true average height of younger women is lessthan that of older women by an amount within the confidenceinterval.Interpret the interval.

(b)

Let

μ₁

denote the population mean height for those aged 20–39 andμ₂ denote the population mean height for thoseaged 60 and older. Interpret the hypotheses

H₀: μ₁ −μ₂ = 1

and

H_a:μ₁ − μ₂ > 1.

The null hypothesis states that the true mean height for olderwomen is 1 inch higher than for younger women. The alternativehypothesis states that the true mean height for older women is morethan 1 inch higher than for younger women.The null hypothesisstates that the true mean height for younger women is more than 1inch higher than for older women. The alternative hypothesis statesthat the true mean height for younger women is 1 inch higher thanfor older women.    The null hypothesis statesthat the true mean height for younger women is 1 inch higher thanfor older women. The alternative hypothesis states that the truemean height for younger women is more than 1 inch higher than forolder women.The null hypothesis states that the true mean heightfor older women is more than 1 inch higher than for younger women.The alternative hypothesis states that the true mean height forolder women is 1 inch higher than for younger women.

Carry out a test of these hypotheses at significance level0.001. Calculate the test statistic and determine theP-value. (Round your test statistic to two decimal placesand your P-value to four decimal places.)

z=

P-value=

(c)

Based on the P-value calculated in (b) would you rejectthe null hypothesis at any reasonable significance level? Explainyour reasoning.

Reject H₀. The data suggests that thedifference in the true average heights exceeds 1.Fail to rejectH₀. The data suggests that the difference inthe true average heights exceeds 1.    RejectH₀. The data does not suggest that thedifference in the true average heights exceeds 1.Fail to rejectH₀. The data does not suggest that thedifference in the true average heights exceeds 1.

(d)

What hypotheses would be appropriate if μ₁referred to the older age group, μ₂ to theyounger age group, and you wanted to see if there was compellingevidence for concluding that the population mean height for youngerwomen exceeded that for older women by more than 1 in.?

H₀: μ₁ −μ₂ = 1
H_a: μ₁ −μ₂ < 1H₀:μ₁ − μ₂ = −1
H_a: μ₁ −μ₂ <−1    H₀:μ₁ − μ₂ = 1
H_a: μ₁ −μ₂ > 1H₀:μ₁ − μ₂ = −1
H_a: μ₁ −μ₂ > −1

You may need to use the appropriate table in the Appendix ofTables to answer this question.