State college is evaluating 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 L=70. For all parts below, explain logic, show all
formulas, include all steps and plug in the numbers (show all work). Explain the decision
to reject or fail (significant or not significant effect).
a. If the writing scores for the population have a standard deviation of O=20, does the
sample provide enough evidence that the new composition course has a significant effect?
Assume a two tailed test with a=.05. Be sure to show all formulas with symbols (and plug in
numbers), steps, processes and calculations for all parts of the answers.
b. If the population standard division is O=10, is the sample sufficient to demonstrate a
significant effect? Again, assume a two-tailed test with a=05. Be sure to show all formulas
with symbols (and plug in numbers), steps, processes and calculations for all parts of the answers.
c. Explain why you reach different conclusions for part (a) and part (b).