Question

In: Statistics and Probability

When the light turns yellow, should you stop or go through it? An article defines the...

When the light turns yellow, should you stop or go through it? An article defines the “indecision zone” as the period when a vehicle is between 2.5 and 5.5 seconds away from an intersection. It presents observations of 750 vehicles passing through various intersections in Vermont for which the light turned yellow in the indecision zone. Of the 750 vehicles, 89 ran a red light.

a) Find a 90% confidence interval for the proportion of vehicles that will run the red light when encountering a yellow light in the indecision zone. Round the answers to three decimal places.

b) Find a 95% confidence interval for the proportion of vehicles that will run the red light when encountering a yellow light in the indecision zone. Round the answers to three decimal places.

c) Find a 99% confidence interval for the proportion of vehicles that will run the red light when encountering a yellow light in the indecision zone. Round the answers to three decimal places.

( ___, ___ )

Solutions

Expert Solution

A) Given data

Sample size (n)=750 (total vehicles)

Number of vehicles ran a red light(x)=89

Sample proportion (p)=x/n

=89/750 =0.1186

p=0.1186

q=1-p=1-0.1186=0.8813

We need to determine the, confidence interval for the proportion of vehicles for the following three confidence levels

a) 90% confidence level

Formula used is

CI=p ± Z×√((p×q)/n)

Z critical value for 90% confidence level is

Z critical value=1.645

CI=0.1186 ± 1.645×√((0.1186×0.8813)/750)

=0.1186 ± 1.645×0.01180

=0.1186 ± 0.0194

Lower limit=0.1186-0.0194=0.0991

Upper limit=0.1186+0.0194=0.138

So ,90% confidence interval is

(0.0991,0.138)

b) 95% confidence level

Z critical value for 95% confidence level is

Z critical value=1.96

CI=0.1186 ± 1.96×√((0.1186×0.8813)/750)

=0.1186 ±1.96×0.01180

=0.1186 ±0.0231

Lower limit=0.1186-0.0231=0.0955

Upper limit=0.1186+0.0231=0.1417

So,95% confidence interval is

(0.0955,0.1417)

c)99% confidence level

Z critical value for 99% confidence level is

Z critical value=2 576

CI=0.1186 ± 2.576×√((0.1186×0.8813)/750)

=0.1186 ± 2.576×0.01180

=0.1186 ±0.0304

Lower limit=0.1186-0.0304=0.0882

Upper limit=0.1186+0.0304=0.149

So,99% confidence interval is

(0.0882,0.149)

orchestra answered 2 years ago
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