20. In a random sample of 325 former prisoners in North Carolina, 29% were arres

Question

20. In a random sample of 325 former prisoners in North Carolina, 29% were arrested again within one year. A 90% confidence interval for the proportion of all North Carolina prisoners who are arrested again within one year is about:

(a) 0.29 ± 0.05 (b) 0.29 ± 0.06 (c) 0.29 ± 0.03 (d) 0.29 ± 0.07 (e) 0.29 ± 0.04

21. In the context of the previous problem, suppose that the confidence interval obtained is too wide. Making use of the information provided in that problem, the minimum sample size required in order to estimate the same population proportion to within two percentage points, still at 90% confidence, is about:

(a) 684 (b) 1393 (c) 481 (d) 894 (e) 1108

Explanation / Answer

Solution:-

20. option (e) 0.29 ± 0.04

Explanation:- 0.29 ± 1.645*sqrt((0.29*(1-0.29)/325) =  0.29 ± 0.0414

21. option (b) 1393

Explanation:- n = (1.645/0.02)^2*0.29*(1-0.29) = 1392.92

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