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 35 two-year colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191. Test the hypothesis, assuming a 5% significance level. Solve using the following steps, similar to Appendix-E (Hypothesios Testing with Two Sample Means). Use the equations for standard error, test statistic and degrees-of-freedom from Section 10.1 of Illowsky (see Two Population Means with unknown Standard Deviations).

a. State the Null Hypothesis (H_o) and Alternate Hypothesis (H_a)

b. Find the random variable X (remember that X is the difference between the two sample means)

c. State the distribution you will use and why ?

d. What is the test statistic (t-value) ?

e. What is the P-value (probability) ? HINT: The formula for the "degrees of freedom" is far more complex. See the formula in Section 10.1.

f. Will you reject or not reject the Null Hypothesis and why ?