An english teacher has been teaching a ninth grade composition class for many years. he has the feeling that over the past several years, the writing ability of students has changed. he would be equally interested in knowing whether writing ability has improved or declined. a national test of proficiency in composition was administered 5 years ago. the resulting distribution of scores was normally shaped and had a mean of 80 and a population standard deviation of 11.4. in order to test his intuition, he samples 41 students from his present class and gives them the same proficiency test. the resulting sample mean is 75.7, and the sample standard deviation is 13.9. answer the following:

a. what is the null hypothesis?

b. what is the alternative hypothesis?

c. what is name of the appropriate statistical test for testing the null hypothesis?

d. what is the obtained value of the appropriate statistic for testing h_0? show your work.

e. using alpha = .05_2tail, what is the appropriate critical value?

f. what is your conclusion about h_0, using alpha = .05_2tail? what is the basis for your decision? in addition to stating whether the null should be rejected or not, say what the conclusion means in the context of the problem.

g. using alpha = .01_2tail, now what is the appropriate critical value?

h. what is your conclusion about h_0, using alpha = .01_2tail? what is the basis for your decision? in addition to stating whether the null should be rejected or not, say what the conclusion means in the context of the problem.

i. calculate and interpret cohen's d.