A student researcher compares the heights of men and women from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 11 men had a mean height of 67.9 inches with a standard deviation of 2.95 inches. A random sample of 17 women had a mean height of 62.9 inches with a standard deviation of 2.62 inches. Determine the 99% confidence interval for the true mean difference between the mean height of the men and the mean height of the women. Assume that the population variances are equal and that the two populations are normally distributed.
Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.