Question

Which inference method?

a. A city planner wants to determine if there is convincing evidence of a difference in the average number of cars passing through two different intersections. He randomly selects $12$times between $6:00$a.m. and $10:00$p.m., and he and his assistant count the number of cars passing through each intersection during the $10$-minute interval that begins at that time.

b. Are more than $75\%$of Toyota owners generally satisfied with their vehicles? Let’s design a study to find out. We’ll select a random sample of $400$ Toyota owners. Then we’ll ask each individual in the sample, “Would you say that you are generally satisfied with your Toyota vehicle?”

c. Are male college students more likely to binge drink than female college students? The Harvard School of Public Health surveys random samples of male and female undergraduates at four-year colleges and universities about whether they have engaged in binge drinking.

d. A bank wants to know which of two incentive plans will most increase the use of its credit cards and by how much. It offers each incentive to a group of current credit card customers, determined at random, and compares the amount charged during the following $6$ months.

Short answer

a. Paired t test for the mean difference

b. One sample z test for a proportion

c. Two sample z test for the difference in proportions

d. Paired t interval for the mean difference

Step-by-step solution

Part (a): Step 1 : Given information

We have given $2$samples for the case study

We have to find a suitable method to determine if the claim that there is a difference in the average number of cars passing through two different intersections is correct or not.

Part (a): Step 2: Explanation

To determine the correctness of the claim, we use hypothesis testing.

Here, we have given $2$samples containing the same $12$times. Also, samples are dependent and are estimated at the mean or average.

Hence, we use a paired t-test for the mean difference.

Part (b): Step 1: Given information

We have given $1$samples for the case study

We have to find a suitable method to determine if the claim that "more than $75\%$Toyota owners are generally satisfied with their vehicles" is true or not.

Part (b): Step 2: Explanation

To determine the correctness of the claim, we use hypothesis testing.

Here, we have given only $1$a sample.

Hence, we use a one-sample test for a proportion.

Part (c): Step 1: Given Information

We have given $2$samples for the case study

We have to find a suitable method to determine if the claim that "male college students are more likely to drink than female college students" is true or not.

Part (c): Step 2: Explanation

To determine the correctness of the claim, we use hypothesis testing.

Here, we have given $2$samples containing different subjects. Hence, samples are independent and are estimated at proportions.

Hence, we use two-sample z tests for the difference in proportions.

Part (d): Step 1: Given information 

We have given $2$samples for the case study

We have to find a suitable method to help the bank to know which of the two incentive plans will most increase the use of its credit cards and by how much

Part (d): Step 2: Explanation

To estimate the difference in the mean amount charged, we use paired testing.

Here, we have given $2$samples containing the same subjects. Hence, samples are dependent and are estimated by paired tests.

Hence, we use a paired t-interval for the mean difference.