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Chapter 10: Q. 53. (page 668)

Happy customers As the Hispanic population in the United States has grown, businesses have tried to understand what Hispanics like. One study interviewed separate random samples of Hispanic and Anglo customers leaving a bank. Customers were classified as Hispanic if they preferred to be interviewed in Spanish or as Anglo if they preferred English. Each customer rated the importance of several aspects of bank service on a 10- point scale.25 Here are summary results for the importance of 鈥渞eliability鈥� (the accuracy of account records, etc.):

Researchers want to know if there is a difference in the mean reliability ratings of all Anglo and Hispanic bank customers.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check that the conditions for performing the test are met.

Short Answer

Expert verified

Part a) The hypothesis is:

H0:渭1=渭2Ha:渭1notequalto渭2

Part b) All conditions are met.

Step by step solution

01

Part a) Step 1: Given information

The given claim that a difference in the means.

02

Part a) Step 2: Explanation

We must now determine the appropriate hypotheses for performing a significance test.

As a result, the claim represents either the null hypothesis or the alternative hypothesis. According to the null hypothesis, the population proportions are equal. If the claim is the null hypothesis, then the alternative hypothesis states the inverse of the null hypothesis.

Therefore, the following are the appropriate hypotheses:

H0:渭1=渭2Ha:渭1notequalto渭2

Where we have,

The true mean reliability rating of all Angle bank customers is 渭1

渭2=represents the true mean reliability rating of all Hispanic bank customers.

03

Part b) Step 1: Explanation

There are three requirements that must be met:

It is satisfying because the samples are drawn at random from different populations.

Independent: It is satisfying because the sample of 92Anglo customers is less than 10%of the total Anglo customer population, and the sample of 86 Hispanic customers is less than 10%of the total Hispanic customer population.

Normal: It is satisfying because both samples are large, with sample sizes of at least 30.

As a result, all of the conditions are met, and a hypothesis test for the mean difference is appropriate.

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Most popular questions from this chapter

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.

Final grades for a class are approximately Normally distributed with a mean of 76and a standard deviation of 8. A professor says that the top10%of the class will receive an A, the next20%a B, the next 40%a C, the next 20%a D, and the bottom 10%an F. What is the approximate maximum grade a student could attain and still receive an F for the course?

a.70b.69.27c.65.75d.62.84e.57

The distribution of grade point averages (GPAs) for a certain college is approximately Normal with a mean of 2.5 and a standard deviation of 0.6. The minimum possible GPA is 0.0 and the maximum possible GPA is 4.33. Any student with a GPA less than 1.0 is put on probation, while any student with a GPA of 3.5 or higher is on the dean鈥檚 list. About what percent of students at the college are on probation or on the dean鈥檚 list?

a.0.6b.4.7c.5.4d.94.6e.95.3

鈥淚 can鈥檛 get through my day without coffee鈥� is a common statement from many college students. They assume that the benefits of coffee include staying awake during lectures and remaining more alert during exams and tests. Students in a statistics class designed an experiment to measure memory retention with and without drinking a cup of coffee 1 hour before a test. This experiment took place on two different days in the same week (Monday and Wednesday). Ten students were used. Each student received no coffee or one cup of coffee 1 hour before the test on a particular day. The test consisted of a series of words flashed on a screen, after which the student had to write down as many of the words as possible. On the other day, each student received a different amount of coffee (none or one cup).

a. One of the researchers suggested that all the subjects in the experiment drink no coffee before Monday鈥檚 test and one cup of coffee before Wednesday鈥檚 test. Explain to the researcher why this is a bad idea and suggest a better method of deciding when each subject receives the two treatments.

b. The researchers actually used the better method of deciding when each subject receives the two treatments that you identified in part (a). For each subject, the number of words recalled when drinking no coffee and when drinking one cup of coffee is recorded in the table. Carry out an appropriate test to determine whether there is convincing evidence that drinking coffee improves memory, on average, for students like the ones in this study.

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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