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 freshman and the writing samples are graded using a standardised evaluation technique. The average score for the sample us M = 76. For the general population of college students, writing scores form a normal distribution with a mean µ = 70.
a) If writing scores for the population have a standard deviation of σ = 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 populations standard deviation is σ =10, is the sample sufficient to demonstrate a significant effect? Again assume a two-tailed test with α = .05.
c) Briefly explain why you reached different conclusions for part (a) and (b).