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Chapter 10: Q.9 (page 663)

Reducing nonresponse? Telephone surveys often have high rates of nonresponse. When the call is handled by voice mail, leaving a message might encourage people to respond when they are called again. Here are data form a study in which (at random) a message was or was not left when voice mail picked up the first call from a survey:

(a) Is this an experiment or an observational study? Justify your answer.

(b) Based on the data, can we conclude that leaving a message increases the proportion of households that are eventually interviewed? Give appropriate statistical evidence to support your answer

Short Answer

Expert verified

a). It is an experiment.

b). Yes, we can conclude that leaving a message increases the proportion of households that are eventually interviewed.

Step by step solution

01

Part (a) Step 1: Given Information

02

Part (a) Step 2: Explanation

An experiment intentionally applies a certain procedure on people to study their reactions. An observational analysis aims to gain details without disrupting the scene they are watching.

03

Part (b) Step 1: Given Information

x1=200

n1=200+91

=291

x2=58

n2=58+42

=100

04

Part (b) Step 2: Explanation

The hypotheses are

H0:p1=p2

H0:p1>p2

The sample proportion is

p^1=x1n1

=200291

=0.6873

p^2=x2n2

=58100

=0.58

p^p=x1+x2n1+n2

=200+58291+100

=0.6598

05

Part (b) Step 3: Explanation

The test statistic is

z=p^1-p^2p^p1-p^p1n1+1n2

=0.6873-0.580.6598(1-0.6598)1291+1100

=1.95

The P-value is the chance of having the value of the test numbers, or a more drastic value.

P=P(Z>1.95)

=P(Z<-1.95)

=0.0256

Reject the null hypothesis if the P-value is lower than the significance level:

localid="1650389579178" P<0.05鈬�RejectH0

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Most popular questions from this chapter

A certain candy has different wrappers for various holidays. During Holiday 1the candy wrappers are 30%silver, 30%red, and 40%pink. During Holiday 2the wrappers are 50%silver and 50%blue. Forty pieces of candy are randomly selected from the Holiday 1distribution, and 40 pieces are randomly selected from the Holiday 2 distribution. What are the expected value and standard deviation of the total number of silver wrappers?

National Park rangers keep data on the bears that inhabit their park. Below is a histogram of the weights of 143bears measured in a recent year.

Which statement below is correct?

(a) The median will lie in the interval (140,180), and the mean will lie in the interval (180,220).

(b) The median will lie in the interval (140,180), and the mean will lie in the interval (260,300).

(c) The median will lie in the interval (100,140), and the mean will lie in the interval (180,220).

(d) The mean will lie in the interval (140,180), and the median will lie in the interval (260,300).

(e) The mean will lie in the interval (100,140), and the median will lie in the interval (180,200).

46. Happy customers As the Hispanic population in the United States has grown, businesses have tried to understand what Hispanics like. One study inter-viewed a random sample of 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. Here are summary results for the importance of 鈥渞eliability鈥� (the accuracy of account records and so on):

(a) The distribution of reliability ratings in each group is not Normal. A graph of the data reveals no outliers. The use of two-sample t procedures is
justified. Why?
(b) Construct and interpret a 95% confidence interval for the difference between the mean ratings of the importance of reliability for Anglo and
Hispanic bank customers.
(c) Interpret the 95% confidence level in the context of this study.

鈥淲ould you marry a person from a lower social class than your own?鈥� Researchers asked this question of a random sample of 385black, never married students at two historically black colleges in the South. Of the 149men in the sample, 91said 鈥淵es.鈥� Among the 236women, 117said 鈥淵es.鈥�14Is there reason to think that different proportions of men and women in this student population would be willing to marry beneath their class?

Holly carried out the significance test shown below to answer this question. Unfortunately, she made some mistakes along the way. Identify as many mistakes as you can, and tell how to correct each one.

State: I want to perform a test of

H0:p1=p2

Ha:p1鈮�p2

at the 95%confidence level.

Plan: If conditions are met, I鈥檒l do a one-sample ztest for comparing two proportions.

  • Random The data came from a random sample of 385 black, never-married students.
  • Normal One student鈥檚 answer to the question should have no relationship to another student鈥檚 answer.
  • Independent The counts of successes and failures in the two groups鈥�91,58,117, and 119鈥�are all at least 10

Do: From the data, p^1=91149=0.61and p^2=117236=0.46.

Test statistic

z=(0.61-0.46)-00.61(0.39)149+0.46(0.54)236=2.91

p=value From Table A, role="math" localid="1650292307192" P(z鈮�2.91)鈮�1-0.3982鈮�0.0018.

Conclude: The p-value, 0.0018, is less than 0.05, so I鈥檒l reject the null hypothesis. This proves that a higher proportion of men than women are willing to marry someone from a social class lower than their own.

Expensive ads Consumers who think a product鈥檚 advertising is expensive often also think the product must be of high quality. Can other information undermine this effect? To find out, marketing researchers did an experiment. The subjects were 90 women from the clerical and administrative staff of a large organization. All subjects read an ad that described a fictional line of food products called 鈥淔ive Chiefs.鈥� The ad also described the major TV commercials that would soon be shown, an unusual expense for this type of product. The 45women who were randomly assigned to the control group read nothing else. The 45in the 鈥渦ndermine group鈥� also read a news story headlined 鈥淣o Link between Advertising Spending and New Product Quality.鈥� All the subjects then rated the quality of Five Chefs products on a seven-point scale. The study report said, 鈥淭he mean quality ratings were significantly lower in the undermine treatment (xA  4.56) than in the control treatment x炉C=5.05;t=2.64,P<0.01.

(a). Explain why the Random and Independent conditions are met in this case.

(b) The distribution of individual responses is not Normal, because there is only a seven-point scale. Why is it still proper to use a two-sample t-test?

(c) Interpret the P-value in context.
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