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.

The category that contributes the largest component to the ${\chi }^2$test statistic is a. White, with $12.4$fewer tickets than expected.

b. White, with $12.4$more tickets than expected.

c. Hispanic, with $6.16$fewer tickets than expected.

d. Hispanic, with $6.16$more tickets than expected.

Short answer

The correct option is (d) i.e. Hispanic, with $6.16$more tickets as compared to expected.

Step-by-step solution

Explanation

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

Explanation

We know that

The null hypothesis asserts that the variables are unrelated, whereas the alternative hypothesis asserts that they are.

$H_0:p_1=0.55,p_2=0.30,p_3=0.08,p_4=0.07$

$H_{\alpha }$represents that at least one $p_i$is incorrect

And expected frequencies are a product of row and column total divided by table total.

And The squared differences between the actual and predicted frequencies, divided by the expected frequency, make up the chi-square subtotals.

White: ${\chi }^2=1.8889$

Black: ${\chi }^2=1.3009$

Hispanic: ${\chi }^2=3.2049$

Other: ${\chi }^2=0.1785$

We can see that the Hispanic group has the highest chi-square subtotal, and hence the Hispanic category contributes the most to the statistic. Furthermore, the observed count ($18$) is $6.16$times higher than the projected count ($11.84$).

Therefore,

Correct option is (d).