Suppose that researchers study a sample of 50 people andfind that 10 are left-handed.
(a) Find a 95% confidence interval for the populationproportion that is left-handed.
(b) What would the confidence interval be if theresearchers used the Wilson value ̃p instead?
(c) Suppose that an investigator tests the nullhypothesis that the population proportion is 18% against thealternative that it is less than that. If α = 0.05 then find thecritical value ˆpc. Using ˆp as the sample estimate, would theinvestigator reject the null? (d) Suppose that researchers areusing this critical value but, unbeknownst to them, the true,population proportion is 0.16. Find the power of thetest.
