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Chapter 10: Q. 91 (page 688)

Two samples or paired data? In each of the following settings, decide whether you should use two-sample t procedures to perform inference about a difference in means or paired t procedures to perform inference about a mean difference. Explain your choice.

a. To test the wear characteristics of two tire brands, A and B, each of 50cars of the same make and model is randomly assigned Brand A tires or Brand B tires.

b. To test the effect of background music on productivity, factory workers are observed. For one month, each subject works without music. For another month, the subject works while listening to music on an MP3 player. The month in which each subject listens to music is determined by a coin toss.

c. How do young adults look back on adolescent romance? Investigators interviewed a random sample of 40couples in their mid-twenties. The female and male partners were interviewed separately. Each was asked about his or her current relationship and also about a romantic relationship that lasted at least 2months when they were aged 15or 16. One response variable was a measure on a numerical scale of how much the attractiveness of the adolescent partner mattered. You want to find out how much men and women differ on this measure.

Short Answer

Expert verified

Part(a) We should use two-sample t procedures to perform inference about a difference in means.

Part(b) We should use paired t procedures to perform inference about a mean difference.

Part(c) We should use paired t procedures to perform inference about a mean difference.

Step by step solution

01

Part(a) Step 1 : Given information

We need to decide whether to use two-sample t procedures or paired t procedures to check inference about a mean difference.

02

Part(a) Step 2 : Simplify

We must use paired t techniques if the two samples contain the same individuals or if the subjects in one sample are related to the subjects in the other sample.
We must use two sample t techniques if the subjects in the two samples are completely unrelated.
Automobiles are randomly assigned to either brand A or brand B in this scenario, resulting in a first sample of brand A cars and a second sample of brand B cars.
Because the cars were randomly assigned to one of the samples, the cars in the two samples will be completely unrelated, making the two sample t methods suitable.


03

Part(b) Step 1 : Given information

We need to decide whether we should use two-sample t procedures to perform inference about a difference in means or paired t procedures to perform inference about a mean difference.

04

Part(b) Step 2 : Simplify

If the two samples contain the same individuals or if the subjects in one sample are connected to the subjects in the other sample, we must employ paired t methods.
If the subjects in the two samples are fully unrelated, we must employ two sample t methods.
For one month, each topic worked with music and for one month, each subject worked without music.
The data for all participants who worked with music for one month is the first sample, while the data for all subjects who worked without music for one month is the second sample.
We should utilise paired t methods because the two samples are the same subjects.

05

Part(c) Step 1 : Given information

We need to decide whether we should use two-sample t procedures to perform inference about a difference in means or paired t procedures to perform inference about a mean difference.

06

Part(c) Step 2 : Simplify

If the two samples contain the same individuals or if the subjects in one sample are connected to the subjects in the other sample, we must employ paired t methods.
If the subjects in the two samples are fully unrelated, we must employ two sample t methods.
We questioned the male and female partners separately in each of the 40couples.
The male partners are in the first sample, while the female partners are in the second.
Because all of the participants in the first sample are male spouses of a subject in the second sample, we should utilise the paired t methods to compare the two samples.

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Most popular questions from this chapter

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.

Friday the 13thRefer to Exercise 88.

a. Construct and interpret a 90%confidence interval for the true mean difference. If you already defined parameters and checked conditions in Exercise 88, you don鈥檛 need to do them again here.

b. Explain how the confidence interval provides more information than the test in Exercise 88.

A survey asked a random sample of U.S. adults about their political party affiliation and how long they thought they would survive compared to most people in their community if an apocalyptic disaster were to strike. The responses are summarized in the following two-way table.

Suppose we select one of the survey respondents at random. Which of the following probabilities is the largest?

a. P(Independent and Longer)

b. P(Independent or Not as long)

c. P(Democrat 3051526=0.200=20.0%| Not as long)

d. P(About as long 3051526=0.200=20.0%| Democrat)

e. P(About as long)

The P-value for the stated hypotheses is 0.002Interpret this value in the context of this study.

a. Assuming that the true mean road rage score is the same for males and females, there is a 0.002probability of getting a difference in sample means equal to the one observed in this study.

b. Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability of getting a difference in sample means at least as large in either direction as the one observed in this study.

c. Assuming that the true mean road rage score is different for males and females, there is a 0.002 probability of getting a difference in sample means at least as large in either direction as the one observed in this study.

d. Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability that the null hypothesis is true.

e. Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability that the alternative hypothesis is true.

Researchers suspect that Variety A tomato plants have a different average yield than Variety B tomato plants. To find out, researchers randomly select10Variety A and10Variety B tomato plants. Then the researchers divide in half each of10small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The10differences (Variety A 鈭� Variety B) in yield are recorded. A graph of the differences looks roughly symmetric and single-peaked with no outliers. The mean difference is x-=0.343051526=0.200=20%x-A-B=0.34and the standard deviation of the differences is s A-B=0.833051526=0.200=20%=sA-B=0.83.Let渭A-B=3051526=0.200=20%渭A鈭払 = the true mean difference (Variety A 鈭� Variety B) in yield for tomato plants of these two varieties.

The P-value for a test of H0: 渭A鈭払=03051526=0.200=20%versus Ha: 渭A鈭払鈮�0 is 0.227. Which of the following is the

correct interpretation of this P-value?

a. The probability that 渭A鈭払 is0.227.

b. Given that the true mean difference (Variety A 鈥� Variety B) in yield for these two varieties of tomato plants is0, the probability of getting a sample mean difference of0.34is0.227.

c. Given that the true mean difference (Variety A 鈥� Variety B) in yield for these two varieties of tomato plants is0, the probability of getting a sample mean difference of0.34or greater is0.227.

d. Given that the true mean difference (Variety A 鈥� Variety B) in yield for these two varieties of tomato plants is0, the probability of getting a sample mean difference greater than or equal to0.34or less than or equal to 鈭�0.34is0.227.

e. Given that the true mean difference (Variety A 鈥� Variety B) in yield for these two varieties of tomato plants is not 0, the probability of getting a sample mean difference greater than or equal to 0.34or less than or equal to 鈭�0.34is0.227.
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