Question

The Chicago Reader is doing some research on the proportion of public transit users that also own

personal motor vehicles, and they're comparing the results between CTA riders and Metra riders. For
their research, they went out on a Monday and recruited a sample of riders on the CTA and the Metra,
and asked them whether they also own a personal motor vehicle. The results are summarized in the
table below
Metra CTA
43 39
22 41
vehicle owners
non-owners
Conduct a hypothesis test to determine whether there is significant statistical evidence (a = 0.05) to
support the claim that riders of the CTA and Metra are not equally likely to own a personal motor

vehicle. Follow the prompts below to complete your test.

What variables are being studied here? Is this a one-sided or two-sided test? Do the variables satisfy

the Central Limit Theorem?

Null hypothesis

Alternative hypothesis:

I

Standard error (remember that in a comparison of two proportions, we use the pooled proportion in this

calculation):

z value for the difference of proportions:

Approximate p-value for the difference:

What is the conclusion of your hypothesis test regarding the initial hypotheses you set up?

Answer 1

The variables being studied are the proportion of public transit users that own personal motor vehicles for CTA riders and Metra riders. This is a two-sided test. The conclusion of the hypothesis test will depend on the calculated p-value.

Step-by-step explanation:

The variables being studied in this question are the proportion of public transit users that own personal motor vehicles for both CTA riders and Metra riders. This is a two-sided test, as we are comparing the proportions for both groups.

To determine whether the variables satisfy the Central Limit Theorem, we need to check if the conditions for each group are met. If both groups have sample sizes greater than or equal to 30 and have at least 10 successes and failures, then the conditions for the Central Limit Theorem are satisfied.

The null hypothesis for this test is that the riders of the CTA and Metra are equally likely to own a personal motor vehicle. The alternative hypothesis is that the riders of the CTA and Metra are not equally likely to own a personal motor vehicle. To conduct the hypothesis test, we use the z test for the difference of proportions and calculate the standard error, z value for the difference, and the approximate p-value.

Based on the test results, if the p-value is less than the significance level of 0.05, we reject the null hypothesis. If the p-value is greater than or equal to 0.05, we do not reject the null hypothesis. The conclusion of the hypothesis test regarding the initial hypotheses will depend on the calculated p-value.