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  3. 5. suppose that researchers study a sample of 50 p

5. Suppose that researchers study a sample of 50 people and find that 10 are left-handed....

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Statistics

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 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 α = 0.05 then find the critical value pˆc. Usingpˆ as the sample estimate, would the investigator reject thenull?

(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.

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