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Chapter 10: Q 6. (page 639)

Broken crackers We don鈥檛 like to find 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. Randomly assign 65newly baked crackers to the microwave and another 65to a control group that is not microwaved. After 1day, none of the microwave group were broken and 16of the control group were broken. Let p1be the true proportions of crackers like these that would break if baked in the microwave and p2be the true proportions of crackers like these that would break if not microwaved. Check if the conditions for calculating a confidence interval forp1-p2met.

Short Answer

Expert verified

It is not suitable to find confidence interval forp1-p2

Step by step solution

01

Given Information

It is given that n1=65

x1=0

n2=65

x2=16

02

Explanation

Testing three conditions for hypothesis test:

Random: As they are assigned, it is satisfied.

Independent: Since all data values in population and used sample, this condition is satisfied.

Normal: There are zero success in first sample, it is not at least 10.

As normal condition is not met, we cannot find confidence intervalp1-p2

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Most popular questions from this chapter

In an experiment to learn whether substance M can help restore memory, the brains of 20rats were treated to damage their memories. First, the rats were trained to run a maze. After a day, 10rats (determined at random) were given substance M and 7of them succeeded in the maze. Only 2of the 10control rats were successful. The two-sample z test for the difference in the true proportions

a. gives z=2.25,P<0.02 .

b. gives z=2.60,P<0.005 .

c. gives z=2.25,P<0.04 but not<0.02

d. should not be used because the Random condition is violated.

e. should not be used because the Large Counts condition is violated.

Literacy A researcher reports that 80%of high school graduates, but only 40%of high school dropouts, would pass a basic literacy test. Assume that the researcher鈥檚 claim is true. Suppose we give a basic literacy test to a random sample of 60high school graduates and a separate random sample of 75high school dropouts.p^G,p^Dbe the sample proportions of graduates and dropouts, respectively, who pass the test.

a. What is the shape of the sampling distribution of p^G-p^D. Why?

b. Find the mean of the sampling distribution.

c. Calculate and interpret the standard deviation of the sampling distribution.

Steroids in high school Refer to Exercise 16.

a. Explain why the sample results give some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

c. What conclusion would you make?

Shrubs and fire Fire is a serious threat to shrubs in dry climates. Some shrubs can

resprout from their roots after their tops are destroyed. Researchers wondered if fire would help with resprouting. One study of resprouting took place in a dry area of Mexico. The researchers randomly assigned shrubs to treatment and control groups. They clipped the tops of all the shrubs. They then applied a propane torch to the stumps of the treatment group to simulate a fire. All 12of the shrubs in the treatment group resprouted. Only 8of the 12shrubs in the control group resprouted.

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

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

Flight times The pilot suspects that the Dubai-to-Doha outbound flight typically takes longer. If so, the difference (Outbound鈭扲eturn) in flight times will be positive on more days than it is negative. What if either flight is equally likely to take longer? Then we can model the outcome on a randomly selected day with a coin toss. Heads means the Dubai-to-Doha outbound flight lasts longer; tails means the Doha-to-Dubai return flight lasts longer. To imitate a random sample of 12days, imagine tossing a fair coin 12times.

a. Find the probability of getting 11or more heads in 12tosses of a fair coin.

b. The outbound flight took longer on 11of the 12days. Based on your result in part (a), what conclusion would you make about the Emirates pilot鈥檚 suspicion?
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