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Chapter 10: Q. 27 (page 625)

Many new products introduced into the market are targeted toward children. The choice behavior of children with regard to new products is of particular interest to companies that design marketing strategies for these products. As part of one study, randomly selected children in different age groups were compared on their ability to sort new products into the correct product category (milk or juice). Here are some of the data:

Age groupNNumber who sorted correctly4- to 5-year-olds50106- to 7-year-olds5328

Are these two age groups equally skilled at sorting? Use information from the Minitab output below to support your answer.

Short Answer

Expert verified

There is sufficient evidence to reject the claim that the two age groups are equally skilled.

Step by step solution

01

Given Information

Given

x1=10

n1=50

x2=28

n2=53

Determine the hypothesis

H0:p1-p2=0

Ha:p1-p2鈮�0

02

Explanation

The sample proportion is the number of successes divided by the sample size:

p^1=x1n1=1050=0.2

p^2=x2n2=2853鈮�0.528

p^p=x1+x2n1+n2=10+2850+53=38103鈮�0.369

Determine the value of the test statistic:

localid="1650451317669" z=p^1-p^2p^p1-p^p1n1+1n2=0.2-0.5280.369(1-0.369)150+153鈮�-3.4

The p-value is the probability of obtaining the value of the test statistic, or a value more extreme. Determine the p-value using table A:

localid="1650451340981" P=P(Z<-3.45orZ>3.45)=2脳P(Z<-3.45)=2脳0.0003=0.0006

If the p-value is smaller than the significance level, reject the null hypothesis:

P<0.05鈬�RejectH0

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Most popular questions from this chapter

A large toy company introduces a lot of new toys to its product line each year. The company wants to predict the demand as measured by y, first-year sales (in millions of dollars) using x, awareness of the product (as measured by the proportion of customers who had heard of the product by the end of the second month after its introduction). A random sample of 65new products was taken, and a correlation of 0.96was computed. Which of the following is a correct interpretation of this value?

(a) Ninety-six percent of the time, the least-squares regression line accurately predicts first-year sales.

(b) About 92%of the time, the proportion of people who have heard of the product by the end of the second month will correctly predict first-year sales.

(c) About 92%of first-year sales can be explained by the proportion of people who have heard of the product by the end of the second month.

(d) The least-squares regression line relating the proportion of people who have heard of the product by the end of the second month and first-year sales will have a slope of 0.96.

(e) Ninety-two percent of the variation in first-year sales can be explained by the least-squares regression line with proportion of people who have heard of the product by the end of the second month as the explanatory variable.

45. Paying for college College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One large university studied this question by asking a random sample of 1296students who had summer jobs how much they earned. The financial aid office separated the responses into two groups based on gender. Here are the data in summary form:

(a) How can you tell from the summary statistics that the distribution of earnings in each group is strongly skewed to the right? A graph of the data reveals no outliers. The use of two-sample t procedures is still justified. why?
(b) Construct and interpret a 90%confidence interval for the difference between the mean summer earnings of male and female students at this university.
(c) Interpret the 90%confidence level in the context of this study.

To study the long-term effects of preschool programs for poor children, researchers designed an experiment. They recruited 123children who had never attended preschool from low-income families in Michigan. Researchers randomly assigned 62of the children to attend preschool (paid for by the study budget) and the other 61 to serve as a control group who would not go to preschool. One response variable of interest was the need for social services as adults. In the past 10years, 38children in the preschool group and 49in the control group have needed social services.

The Minitab output below gives a 95% con铿乨ence interval for p1-p2. Interpret this interval in context. Then explain what additional information the con铿乨ence interval provides.

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.

A fast-food restaurant uses an automated filling machine to pour its soft drinks. The machine has different settings for small, medium, and large drink cups. According to the machine鈥檚 manufacturer, when the large setting is chosen, the amount of liquid dispensed by the machine follows a Normal distribution with mean 27ounces and standard deviation 0.8ounces. When the medium setting is chosen, the amount of liquid dispensed follows a Normal distribution with mean 17ounces and standard deviation 0.5ounces. To test the manufacturer鈥檚 claim, the restaurant manager measures the amount of liquid in a random sample of 25cups filled with the medium setting and a separate random sample of 20 cups filled with the large setting. Let x1-x炉2be the difference in the sample mean amount of liquid under the two settings (large 鈥� medium). Find the probability thatx炉1-x炉2 is more than 12 ounces. Show your work.
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