Suppose that researchers study a sample of 50 people and findthat 10 are left-handed.
(a) Find a 95% confidence interval for the population proportionthat is left-handed.
(b) What would the confidence interval be if the researchersused the Wilson value ~p instead?
(c) Suppose that an investigator tests the null hypothesis thatthe population proportion is 18% against the alternative that it isless than that. If = 0:05 then nd the critical value ^pc. Using ^pas the sample estimate, would the investigator reject the null?
(d) Suppose that researchers are using this critical value but,unbeknownst to them, the true, population proportion is 0.16. Findthe power of the test.
