14. A confidence interval program for the population proportion of p 5 produced

Question

14. A confidence interval program for the population proportion of p 5 produced the graph given below Although most conidence intervals cover the population proportion p 0.5, some do not. 0.0 0.2 0.4 0.6 0.8 1.0 The coverage rate (confidence level) of these confidence intervals is approximately: (a) .94 (b) .86 (c) s8 (d) .90 (e) .95 15-17. According to a study published in the Journal of Economic Perspectives (2014), roughly 12 percent of humans are left-handed. Let p denote the proportion of left-handed childern in a random sample of 144 school children. 15. The standard deviation of p is closest to: (a).001 (b).022 (c).027 (d) .049 (e) .059 16. The probability that the sample proportion is at most 0.14 is closest to: (a) .12 (b) .46 (c).88 (d) .54 (e).77 17. The probability that the sample proportion is within plus/minus 0.02 of the population proportion of 0.12 is closest to: (a) .12 (b) 46 (c) .88 (d) .54 (e) .77 18. A study is being planned to estimate the incidence of sexual assault at a university with a margin of error of 0.04 and at a confidence level of 0.96. Assume that the incidence of sexual assault is at most 0.30. What is minimum sample size necessary to achieve this goal? (a) 106 (b) 213 (c) 420 (d) 554 (e) 859

Explanation / Answer

Result:

18).

P=0.3

For 96%, z=2.054

d=0.04

Sample size = (z2*p*(1-p))/d2

= (2.0542*0.3*0.7)/0.042

=553.7

The sample size required= 554.

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