Question

The mean annual tuition and fees for a sample of 12 private colleges was with a standard deviation of . You wish to test whether the mean tuition and fees for the population of all private colleges is greater than . Calculate the test statistic value and give its P-value for this test. Assume the population is normally distributed.

Group of answer choices

t = 2.38; 0.01 < P-value < 0.025

t = 2.38; 0.01 < P-value < 0.02

z = 2.38; P-value = 0.0087

z = 2.38; P-value = 0.0174

t = 2.38; 0.02 < P-value < 0.05

Answer 1

Since we are not provided with the population standard deviation, we will be using a "" test statistic and its value will be 2.38, as given in the options. Since the sample size (n) is 12, the degrees of freedom will be = n - 1 = 11. We are dealing with a "greater than" alternative hypothesis here, so while calculating the p-value, we will be concerned with the right tail probability.
The p-value will be = P(t₁₁ > 2.38) = 0.0183.

Hence, our answer is -> t = 2.38; 0.01 < P-value < 0.02 (or, t = 2.38; 0.01 < P-value < 0.025).