Question

A student researcher compares the heights of American students and non-American students from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 1818 American students had a mean height of 68.168.1 inches with a standard deviation of 3.133.13 inches. A random sample of 1212 non-American students had a mean height of 64.364.3 inches with a standard deviation of 1.841.84 inches. Determine the 99%99% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1: Find the point estimate that should be used in constructing the confidence interval.

Step 2: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 3: Construct the 99%99% confidence interval. Round your answers to two decimal places.

Answer 1

The statistical software output for this problem is:

Step -1: Point estimate = 3.8

Step - 2: Margin of error = (6.5782232 - 1.021777)/2 = 2.778223

Step - 3: 99% confidence interval:

(1.02, 6.58)