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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

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.

Let pM,pFbe the proportions of all college males and

females who worked last summer. The hypotheses to be tested are

a. H0:pM-pF=0versesHa:pM-pF鈮�0

b. H0:pM-pF=0versesHa:pM-pF>0

c. H0:pM-pF=0versesHa:pM-pF<0

d. H0:pM-pF>0versesHa:pM-pF=0

e.H0:pM-pF鈮�0versesHa:pM-pF=0

Artificial trees? An association of Christmas tree growers in Indiana wants to know if there is a difference in preference for natural trees between urban and rural households. So the association sponsored a survey of Indiana households that had a Christmas tree last year to find out. In a random sample of 160rural households, 64had a natural tree. In a separate random sample of 261urban households, 89had a natural tree. A 95%confidence interval for the difference (Rural 鈥� Urban) in the true proportion of households in each population that had a natural tree is -0.036to0.154. Does the confidence interval provide convincing evidence that the two population proportions are equal? Explain your answer.

An agricultural station is testing the yields for six different varieties of seed corn. The station has four large fields available, located in four distinctly different parts of the county. The agricultural researchers consider the climatic and soil conditions in the four parts of the county as being quite different, but are reasonably confident that the conditions within each field are fairly similar throughout. The researchers divide each field into six sections and then randomly assign one variety of corn seed to each section in that field. This procedure is done for each field. At the end of the growing season, the corn will be harvested, and the yield (measured in tons per acre) will be compared. Which one of the following statements about the design is correct?

a. This is an observational study because the researchers are watching the corn grow.

b. This a randomized block design with fields as blocks and seed types as treatments.

c. This is a randomized block design with seed types as blocks and fields as treatments.

d. This is a completely randomized design because the six seed types were randomly assigned to the four fields.

e. This is a completely randomized design with24迟谤别补迟尘别苍迟蝉鈥�6 seed types and 4 fields.

At a baseball game, 42of 65randomly selected people own an iPod. At a rock concert occurring at the same time across town, 34of 52randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90%confidence interval for the difference (Game 鈭� Concert) in population proportions is (鈭�0.154,0.138). Which of the following gives the correct outcome of the researcher鈥檚 test of the claim?

a. Because the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is the same.

b. Because the center of the interval is -0.008, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

c. Because the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different.

d. Because the confidence interval includes more negative than positive values, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

e. The researcher cannot draw a conclusion about a claim without performing a significance test.
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