Question

Sixteen percent of drivers registered in New Jersey are black. Of the 324 speeding tickets issued in one month on the NJ Turnpike, 25% went to black drivers. Is the percentage of speeding tickets issued to blacks unusually high compared with the state's registration information? Use the alpha = 0.05 level of significance

Answer 1

Solution:

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:

Null hypothesis: H0: The percentage of speeding tickets issued to blacks is 16%.

Alternative hypothesis: Ha: The percentage of speeding tickets issued to blacks is greater than 16%.

H0: p = 0.16 versus Ha: p > 0.16

This is an upper tailed test.

We are given

Level of significance = α = 0.05

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 = 324

p̂ = x/n = 0.25

p = 0.16

q = 1 - p = 0.84

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.25 - 0.16)/sqrt(0.16*0.84/324)

Z = 0.09 / 0.0204

Z = 4.4189

Test statistic = 4.4189

P-value = 0.0000

(by using z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the percentage of speeding tickets issued to blacks is unusually high compared with the state's registration information.