An insurance company has a complaint department where customers can call and speak to a representative.

The company claims that the average time they keep their customers "on hold" before they reach a human is

only 15 minutes with an SD = 7 minutes. I believe the true average hold time is much higher, even more than

17.5 minutes, so I choose HA: True Average > 15 minutes and assume the SD is still 7 minutes. To test their

claim, I plan to call the complaint department at 25 randomly selected times and record the average time I'm

kept on hold.

a) What test should you consider? (Hint: if nothing is specified, then SD means population standard

deviation. s is called sample standard deviation or sample SD.)

b) What is the standard deviation of x?

c) Assuming a = 17.5, what is the effect size?

d) What is the critical value for = 0.05?

e) What is the power for this a? And what are the type I and type II errors?

f) If I would like to conduct another test to make the power at least 90% for this a. What is the minimal

sample size?

g) What is the minimal sample size to make the type II error no more than 1%?

h) What is the minimal sample size for a 95% CI with a margin of error no greater than 1?

i) Now we assume the sample standard deviation is 7, and we no longer know the population SD. What is

the minimal sample size to achieve 90% power for a = 17.5? What if we change the alternative to

two-sided, is your minimal sample size changed as well? If so, what is the new minimal sample size?

Use R for this part and attach the output.

j) Compare your results for (f) and (i). What do you find? Can you explain it?