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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 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 deviation0.8ounces. 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 20cups filled with the large setting. Let x炉1-x炉2be the difference in the sample mean amount of liquid under the two settings (large 鈥� medium). Find the mean and standard deviation of the sampling distribution.

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Acupuncture
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Is the pregnancy rate significantly higher for women who received acupuncture? To find out, researchers perform a test of H0:P1=P2versus H伪;P1>P2, whereP1&P2are the actual pregnancy rates for women like those in the study who do and don't receive acupuncture, respectively.

(a) Name the appropriate test and check that the conditions for carrying out this test are met.

(b) The appropriate test from part (a) yields a P-value of 0.0152Interpret thisP-value in context.

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(d) What flaw in the design of the experiment prevents us from drawing a cause-and-effect conclusion? Explain.

Dr Teresa Amabile conducted a study involving 47college students, who were randomly assigned to two treatment groups. The 23students in one group were given a list of statements about external reasons (E) for writing, such as public recognition, making money, or pleasing their parents. The 24students in the other group were given a list of statements about internal reasons (I) for writing, such as expressing yourself and enjoying playing with words. Both groups were then instructed to write a poem about laughter. Each student鈥檚 poem was rated separately by 12different poets using a creativity scale. The 12poets鈥� ratings of each student鈥檚 poem were averaged to obtain an overall creativity score. We used Fathom software to randomly reassign the 47subjects to the two groups 1000times, assuming the treatment received doesn鈥檛 affect each individual鈥檚 average creativity rating. The dot plot shows the approximate randomization distribution of x1-xE

(a) Why did researchers randomly assign the subjects to the two treatment groups?

(b) In the actual experiment, x1-xE=4.15. What conclusion would you draw? Justify your answer with appropriate evidence.

(c) Based on your conclusion in part (b), could you have made a Type I error or a Type II error? Justify your answer.

Coaching and SAT scores (10.2) What we really want to know is whether coached students improve more than uncoached students and whether any advantage is large enough to be worth paying for. Use the information above to answer these questions:

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24005521142622439078

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