A transportation analyst is interested in determining the proportio the light ha

Question

A transportation analyst is interested in determining the proportio the light has turned yellow when they were in the "indecision z from the intersection) of drivers who run a red light after (a)in the absece of preliminary data, how large a sample must be specify the proportion to within ± 0.04. taken to ensure that a 95% CI will (b)Of 710 vehicles sampled in a traffic study, 8s ran a red light. Construct a drivers who run a red light after the light has turned yellow when they were in the "indecision zone" (c)Based on the data above estimate the sample size needed so th proportion to within ±0.05 at the 95% CI will specify the

Explanation / Answer

Solution

(a) Let p = 0.5

We know that Margin of error = +-0.04

i.e. +-1.96((0.5)(0.5)/n)0.5 = +-0.04

n = 600

(b) now p = 85/710 = 0.1197

95% CI = (0.1197+-1.96((0.1197)(0.8803)/710)0.5

95% CI = (0.0958,0.1436)

(c) Margin of error = +-0.05

+-0.05 = 1.96((0.1197)(0.8803)/n)0.5

n = 162

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