5. Suppose that researchers study a sample of 50 people and findthat 10 are left-handed. (a) Find a 95% confidence interval for thepopulation proportion that is left-handed. (b) What would theconfidence interval be if the researchers used the Wilson value ̃pinstead? (c) Suppose that an investigator tests the null hypothesisthat the population proportion is 18% against the alternative thatit is less than that. If α = 0.05 then find the critical value ˆpc.Using ˆp as the sample estimate, would the investigator reject thenull? (d) Suppose that researchers are using this critical valuebut, unbeknownst to them, the true, population proportion is 0.16.Find the power of the test.
