Final answer:
In this case, the confidence interval is (1.61184, 1.98816), meaning we are 95% confident that the true difference in heights falls within this range.
Step-by-step explanation:
To calculate the confidence interval for the difference between the population mean heights of younger and older women, we can use the formula:
Confidence Interval = (mean of sample 1 - mean of sample 2) ± (critical value × standard error)
In this case, sample 1 represents the heights of women aged 20-39 (mean = 64.9) and sample 2 represents the heights of women aged 60 and older (mean = 63.1).
Using the given data, the standard error for sample 1 is 0.096 and for sample 2 is 0.11. Since the sample sizes (n1 = 866, n2 = 934) are large, we can assume that the sampling distributions of the sample means are approximately normal.
Next, we need to find the critical value for a 95% confidence level. This value can be obtained from a standard normal distribution table or a calculator. For a 95% confidence level, the critical value is approximately 1.96.
Now, we can calculate the confidence interval:
(64.9 - 63.1) ± (1.96 × 0.096) = 1.8 ± 0.18816 = (1.61184, 1.98816)
This means that we are 95% confident that the true difference between the population mean height for younger women and that for older women falls within the range of 1.61184 inches to 1.98816 inches.
Your question is incomplete, but most probably the full question was:
The National Health Statistics Reports dated Oct. 22, 2008, included the following information on the heights (in.) for non-Hispanic white females:
Age Sample Size Sample Mean Std. Error Mean
20-39 866 64.9 .09
60 and older 934 63.1 .11
Calculate and interpret 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.