Question

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. conduct a hypothesis test at the 5% level. note: if you are using a student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (in general, you must first prove that assumption, though.)

Answer 1

To conduct a hypothesis test, compare the mean enrollments at two-year and four-year colleges. If the p-value is less than 0.05, conclude that the mean enrollment at four-year colleges is higher.

Step-by-step explanation:

To conduct a hypothesis test at the 5% level, we need to compare the mean enrollments at two-year and four-year colleges. The null hypothesis (H0) is that the mean enrollment at four-year colleges is not higher than at two-year colleges, while the alternative hypothesis (Ha) is that the mean enrollment at four-year colleges is higher.

Using the data provided, we can calculate the test statistic by subtracting the mean enrollment of two-year colleges from the mean enrollment of four-year colleges and dividing by the standard error of the difference. The standard error of the difference is found by taking the square root of the sum of the squared standard deviations divided by the sample size.

Using the calculated test statistic, we can find the p-value from the t-distribution table. If the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the mean enrollment at four-year colleges is higher than at two-year colleges.