Question

2) A student at a four-year college claims that mean enrollment at four–year colleges is higher than at two–year colleges in the United States. Two surveys are conducted. Of the 19 four-year colleges surveyed, the mean enrollment was 5,892 with a standard deviation of 6,134. Of the 21 two–year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 2,777. Test her claim using α = 0.05, assume the populations are normal; and variances are unknown and unequal. Find 99% confidence interval for means difference and interpret it.

Then question 2 for the case when the variances are unknown and equal.

Answer 1

2a) H0: The mean enrollment at four–year colleges is not higher than at two–year colleges in the United States.

H1: The mean enrollment at four–year colleges is higher than at two–year colleges in the United States.

Let the los be alpha = 0.05

Critical t: 1.709384
P-Value: 0.2978

Here t value is less than t critical value so we accept H0

or P-value > alpha 0.05 so we accept H0

Thus we conclude that The mean enrollment at four–year colleges is not higher than at two–year colleges in the United States.

b)