A report included the following information on the heights (in.) for non-Hispani

Question

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

(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 20–39 60 and older.) , Interpret the interval

(b) Let 1 denote the population mean height for those aged 20–39 and 2 denote the population mean height for those aged 60 and older. Interpret the hypotheses H0: 1 2 = 1 and Ha: 1 2 > 1.

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 to two decimal places and your P-value to four decimal places.)

(c) Based on the P-value calculated in (b) would you reject the null hypothesis at any reasonable significance level? Explain your reasoning.

(d) What hypotheses would be appropriate if 1 referred to the older age group, 2 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 more than 1 in.?

Age Sample
Size Sample
Mean Std. Error
Mean 20–39 868 65.9 0.09 60 and older 934 64.3 0.11

Explanation / Answer

(a) 95% confidence interval : (20–39 60)+-z0.025(0.092+0.112)0.5

= (65.9-64.3)+-1.96*0.14213

=(1.3214, 1.8786)

(b) H0: 1 2 = 1 and Ha: 1 2 > 1

Z test statistic = ((65.9-64.3)-1)/(0.092+0.112)0.5 = 4.22

p value = 0.000012

(c) Reject the null hypothesis as p value < 0.001

(d) H0: 2 1 = 1 and Ha: 2 1 > 1

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