Question

1. The confidence interval of population propor- tion obtained from x = 120 and n = 500 at the 99% level of confidence is a. 24% +5%. b. 5% + 24% c. 24% +2.5%. d. 24% + 1%. e. 99% +24%.

Answer 1

2)

sample proportion, = 0.24
sample size, n = 500
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.24 * (1 - 0.24)/500) = 0.0191

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

Margin of Error, ME = zc * SE
ME = 2.58 * 0.0191
ME = 0.05 = +/- 5

OPtion b) is Correct

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