Question

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	64.7	0.09
60 and older	933	63.2	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 μ_20–39 − μ_{60 and older}.)

Interpret the 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.  

  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.

(b) Let μ₁ denote the population mean height for those aged 20–39 and μ₂ denote the population mean height for those aged 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 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.

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 younger women is 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women.

The null hypothesis states that the true mean height for older women is 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is more than 1 inch higher than for younger 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 to two decimal places and your P-value to four decimal places.)

Answer 1

a) 95% CI for difference: (1.219, 1.781)

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.

b) The null hypothesis states that the true mean height for younger women is 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women.

For testing, we use independent sample t test assuming equal variance.

WE obtain

Value of t statistic = 3.49 with DF=1794 and P-Value = 0.0002
We have used Pooled StDev = 3.0370
Thus we fail to reject the null at  significance level 0.001.