Question

7. A city claims that less than 50% of drivers favor using red light cameras. In a survey of 500 drivers, 47% say
they are in favor of red light cameras. Test the claim at the .01 level of significance (α=.01) using the p-value
method.

Answer 1

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

H₀: p = 0.50 versus H_a: p < 0.50

This is a lower tailed test.

We are given

Level of significance = α = 0.01

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

n = sample size = 500

p̂ = x/n = 0.47

p = 0.5

q = 1 - p = 0.5

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.47 - 0.50)/sqrt(0.5*0.5/500)

Z = -1.3416

Test statistic = -1.3416

P-value = 0.0899

(by using z-table)

P-value > α = 0.01

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that less than 50% of drivers favor using red light cameras.