The investigators plan to use a sample of size 60

to carry out tests of hypotheseswith the null hypothesis=250 .

They think the population standard deviation is equal to50 .

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

Use Rpwr.t.testfrom thepwrpackage or similar functions.

5.1If the investigators use=.05 and a one-sided alternative hypothesis<250,

what is the power of the test?Show how you found the answer.

5.2If the investigators use=.05 and a two-sided alternative hypothesis 250,

what is the power of the test?Show how you found the answer.

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

5.4Assume 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=.05 ?Continue to use 50 as an estimate of the population standard deviation.Show how you found the answer.

5.5Assume 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=.05 ?Continue to use 50 as an estimate of the population standard deviation.Show how you found the answer.

5.6Compare your answers to questions 5.4 and 5.5 and comment on the difference.