Question: State College is evaluating a new English composition course for freshmen. A random sample of n = 25 freshmen is obtained and the students are placed in the course during their first semester. One year later, a writing sample is obtained for each student and the writing samples are graded using a standardized evaluation technique. The average score for the sample is M = 76. For the general population of college students, writing scores form a normal distribution with a mean of µ = 70.

a. If the writing scores for the population have a standard deviation of ? = 20, does the sample provide enough evidence to conclude that the new composition course has a significant effect? Assume a two-tailed test with α = .05.

b. If the population standard deviation is ? = 10, is the sample sufficient to demonstrate a significant effect? Again, assume a two-tailed test with α = .05.

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