Question: State College is evaluation a new English composition course for freshman. A random sample of n= 25 freshman 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 m = 70.

a. If the writing scores for the population have a standard deviation of s = 20, does the sample provide enough evidence to conclude that the new composition course has a significant effect?

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

c. Briefly explain why you reached different conclusions for part (a) and part (b).