In: Statistics and Probability
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 18 American students had a mean height
of 70 inches with a standard deviation of 3.03 inches. A
random
sample of 12 non-american students had a mean height of 66.1 inches
with a standard deviation of 2.35 inches. Determine the 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. Find
the margin of error to be used in constructing the confidence
interval.