Question: State college is evaluating a new English composition course for freshmen. A random sample for n=25 is obtained and the students are placed in the course during the 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 u=70.

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

Assume a two tailed test with a=.05.

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

c. Briefly explain why you reached different conclusions for a&b.