Hypothesis testing for single population mean.
State College is evaluating a new English composition course for freshmen. A random sample of n = 25 freshmen is obtained and students are placed in course throughout their first semester. One year later, a writing sample is obtained for each student and 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 mean of m = 70.
a. If the writing scores for the population have the standard deviation of s = 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 = 0.05.
b. If the population standard deviation is s = 10, is the sample sufficient to show a significant effect? Again, assume a two-tailed test with a = 0.05.
c. in brief explain why you reached different conclusions for part (a) and part (b).