1.The investigators plan to use a sample of size 60

to carry out tests of hypotheses with the null hypothesis = 250. They think the population standard deviation is equal to 50 .

They really want their hypothesis tests to correctly reject the null hypothesis if = 235. Use R

pwr.t.test from the pwr package or similar functions.

1.1If the investigators use = 0.05 and a one-sided alternative hypothesis < 250, what is

the power of the test? Show the details of how you found the answer.

1.2If the investigators use = 0.05 and a two-sided alternative hypothesis = 250, what is

the power of the test? Show how you found the answer

1.3Compare your answers to questions 5.1 and 5.2 and comment on the difference. Include

specic and relevant details.

1.4Assume that the population mean really is 235. What size sample would be needed to have 90% power to correctly reject the null hypothesis = 250 if the investigators use a one-sided alternative hypothesis < 250, using = 0.05 ? Continue to use 50 as an

estimate of the population standard deviation. Show how you found the answer

1.5Assume that the population mean really is 235. What size sample would be needed to have 90% power to correctly reject the null hypothesis = 250 if the investigators use a two-sided alternative hypothesis = 250, using = 0.05 ? Continue to use 50 as an

estimate of the population standard deviation. Show how you found the answer.

1.6Compare your answers to questions 5.4 and 5.5 and comment on the difference. Include specics and relevant results