Power calculations

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.

A. If the investigators use = .05 and a one-sided alternative hypothesis < 250, what is the power of the test?

- Show R code functions used

- Show full working in terms of how you got the answer

B. If the investigators use = .05 and a two-sided alternative hypothesis 250, what is the power of the test?

- Show R code functions used

- Show full working in terms of how you got the answer

C. Compare your answers from Q1 and 2. Is there a difference in achieved power when using a one sided vs. two-sided hypothesis test? Provide a detailed explanation