A large 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 a 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.

Question: 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 and attach your output.