Textbook Problem

A local college requires an English composition course for all freshmen. This year they are evaluating a new online version of the course. A random sample of n = 16 freshmen is selected and the students are placed in the online course. At the end of the semester, all freshmen take the same English composition exam. The average score for the sample is M = 76. For the general population of freshmen who look the traditional lecture class, the exam scores form a normal distribution with a mean of $\mu$ = 80.

a. If the final exam scores for the population have a standard deviation of $\sigma$ = 12, does the sample provide enough evidence to conclude that the new online course is significantly different from the traditional class? Assume a two-tailed test with $\alpha$ = .05.

c. If the population standard deviation $\sigma$ = 6, is the sample sufficient to demonstrate a significant difference? Again, assume a two-tailed test with $\alpha$ = .05.

c. Comparing your answers for pans a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.