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Chapter 10: Q. 100 (page 691)

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 12times between 6:00a.m. and 10:00p.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鈥檚 design a study to find out. We鈥檒l select a random sample of 400 Toyota owners. Then we鈥檒l ask each individual in the sample, 鈥淲ould you say that you are generally satisfied with your Toyota vehicle?鈥�

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

Expert verified

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

01

Part (a): Step 1 : Given information

We have given 2samples 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.

02

Part (a): Step 2: Explanation

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

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

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

03

Part (b): Step 1: Given information

We have given 1samples 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.

04

Part (b): Step 2: Explanation

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

Here, we have given only 1a sample.

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

05

Part (c): Step 1: Given Information

We have given 2samples 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.

06

Part (c): Step 2: Explanation

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

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

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

07

Part (d): Step 1: Given information 

We have given 2samples 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

08

Part (d): Step 2: Explanation

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

Here, we have given 2samples 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.

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Most popular questions from this chapter

Which of the following will increase the power of a significance test?

a. Increase the Type II error probability.

b. Decrease the sample size.

c. Reject the null hypothesis only if the P-value is less than the significance level.

d. Increase the significance level 伪.

e. Select a value for the alternative hypothesis closer to the value of the null hypothesis.

Digital video disks A company that records and sells rewritable DVDs wants to compare the reliability of DVD fabricating machines produced by two different manufacturers. They randomly select 500DVDs produced by each fabricator and find that 484of the disks produced by the first machine are acceptable and 480of the disks produced by the second machine are acceptable. If p1,p2are the proportions of acceptable DVDs produced by the first and second machines, respectively, check if the conditions for calculating a confidence interval for p1-p2are met.

American-made cars Nathan and Kyle both work for the Department of Motor Vehicles (DMV), but they live in different states. In Nathan鈥檚 state, 80%of the registered cars are made by American manufacturers. In Kyle鈥檚 state, only 60%of the registered cars are made by American manufacturers. Nathan selects a random sample of 100cars in his state and Kyle selects a random sample of 70cars in his state. Let pn-pkbe the difference (Nathan鈥檚 state 鈥� Kyle鈥檚 state) in the sample proportion of cars made by American manufacturers.

a. What is the shape of the sampling distribution of pn-pk? Why?

b. Find the mean of the sampling distribution.

c. Calculate and interpret the standard deviation of the sampling distribution.

A researcher wants to determine whether or not a 5-week crash diet is effective over a long period of time. A random sample of 15five-week crash dieters is selected. Each person鈥檚 weight (in pounds) is recorded before starting the diet and 1year after it is concluded. Do the data provide convincing evidence that 5-week crash dieters weigh less, on average, 1year after finishing the diet?

Suppose the probability that a softball player gets a hit in any single at-bat is 0.300. Assuming that her chance of getting a hit on a particular time at bat is independent of her other times at bat, what is the probability that she will not get a hit until her fourth time at bat in a game?

a.(43)(0.3)1(0.7)33051526=0.200=20.0%43(0.3)1(0.7)3

b.(43)(0.3)3(0.7)13051526=0.200=20.0%43(0.3)3(0.7)1

C.(41)(0.3)3(0.7)13051526=0.200=20.0%41(0.3)3(0.7)1

d.(0.3)3(0.7)13051526=0.200=20.0%(0.3)3(0.7)1

e.(0.3)1(0.7)33051526=0.200=20.0%(0.3)1(0.7)3
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