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

a. If writing scores for population have standard deviation of σ = 20, does sample give adequate evidence to conclude that new composition course has significant effect?

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

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