A psychology department chair notices that the average number of student complaints the department receives per week is 1.4 times and a standard deviation of 1.6 times. He notices that the department has made some poor policy changes recently and wants to see if the number of complaints that the department receives has increased. He records the following number of complaints that came in per week for the past eight weeks:
2, 4, 3, 5, 4, 1, 1, 4

a) Given the above information and a 5% alpha level, first choose an appropriate test to answer the question "if there are now more complaints". Then list the hypotheses.

b) Calculate the test statistics

c) What conclusion can you make from your calculation? Make it clear that what your conclusion means regarding the research question.

d) Compute the Cohen's d coefficient and comment on the effect size.

e) Write down the FORMAL conclusion (p value should be calculated).

f) What is a Type I error and what is a Type II error in this context?