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Chapter 10: Q.10 (page 622)

Explain why the conditions for using two-sample z procedures to perform inference about p1-p2are not met in the settings

Broken crackers We don鈥檛 like to 铿乶d broken crackers when we open the package. How can makers reduce breaking? One idea is to microwave the crackers for 30seconds right after baking them. Breaks start as hairline cracks called 鈥渃hecking.鈥� Assign 65newly baked crackers to the microwave and another 65to a control group that is not microwaved. After one day, none of the microwave group and 16 of the control group show checking.8

Short Answer

Expert verified

From the given information,

The success rate in the first sample, i.e. the microwave group, is 0(less than 10). It means that the normalcy assumption isn't met in this case.

As a result, the two-proportion z-test is inappropriate in this situation.

Step by step solution

01

Given Information

It is given in the question that, the values arex1=0,n1=65,x2=16,n2=65

02

Step 2: Explanation

The number of successes in both samples must be greater than 10to execute the two-proportion z-test.

The success rate in the first sample, i.e. the microwave group, is 0(less than 10). It means that the normalcy assumption isn't met in this case.

As a result, the two-proportion z-test is inappropriate in this situation.

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Most popular questions from this chapter

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.

Let Xrepresent the score when a fair six-sided die is rolled. For this random variable,渭X=3.5 and 蟽X=1.71. If the die is rolled 100times, what is the approximate probability that the total score is at least375?

Refer to Exercise 36. Suppose we select independent SRSs of 16 young men and 9 young women and calculate the sample mean heights xMandxW

(a) Describe the shape, center, and spread of the sampling distribution of xM-xW

(b) Find the probability of getting a difference in sample means x炉M-x炉Wthat鈥檚 greater than or equal to 2inches. Show your work.

(c) Should we be surprised if the sample mean height for the young women is more than 2inches less than the sample mean height for the young men? Explain.

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).

Construct and interpret a 95% confidence interval for p1-p2 in Exercise 23. Explain what additional information the confidence interval provides.
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