Question

A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race or ethnicity of the driver. The results are summarized in the following table.

The proportion of this city's population in each of the racial/ethnic categories listed is as follows.

We wish to test $H_0$: The racial/ethnic distribution of traffic tickets in the city is the same as the racial/ethnic distribution of the city's population.

We compute the value of the ${\chi }^2$test statistic to be $6.57$. Assuming that the conditions for inference are met, which of the following is the correct P-value?

a. Greater than$0.20$

b. Between $0.10$and$0.20$

c. Between $0.05$and$0.10$

d. Between $0.01$and$0.05$

e. Less than$0.01$

Short answer

The correct option is (c) i.e. between$0.05$and$0.10$.

Step-by-step solution

Given information

We need to find the correct option for the given data.

Explanation

We know that

${\chi }^2=6.57$

And White, Black, Hispanic, and Other are the four-race categories in the variable race.

The number of categories has been reduced by one degree of freedom:

$df=3$

The P-value is the chance of getting the test statistic's value, or a number that is more extreme. The P-value in the chi-square distribution table in the appendix containing the ${\chi }^2$-value in the row $df=3$is the number (or interval) in the column title:

$0.05<P<0.10$

Therefore,

Correct option is (c).