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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 10: Q 8. (page 640)

Digital video disks A company that records and sells rewritable DVDs wants to compare the reliability of DVD fabricating machines produced by two different manufacturers. They randomly select $500$ DVDs produced by each fabricator and find that $484$ of the disks produced by the first machine are acceptable and $480$ of the disks produced by the second machine are acceptable. If $p_{1}, p_{2}$ are the proportions of acceptable DVDs produced by the first and second machines, respectively, check if the conditions for calculating a confidence interval for $p_{1} - p_{2}$ are met.

Short Answer

Expert verified

All conditions are satisfied, we can find confidence interval.

Step by step solution

01

Given Information

It is given that $n_{1} = 500$

$x_{1} = 484$

$n_{2} = 500$

$x_{2} = 480$

02

Explanation

Three conditions for hypothesis test are:

Random: As assigned randomly, it is satisfied.

Independent: As all data values in population and used sample, it is satisfied.

Normal: Success in first sample is $484$ , and failures are $500 - 484 = 16$ , both are greater than ten , it is also satisfied.

All conditions are met, we can find confidence interval for $p_{1} - p_{2}$

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Most popular questions from this chapter

The P-value for the stated hypotheses is $0.002$ Interpret this value in the context of this study.

a. Assuming that the true mean road rage score is the same for males and females, there is a $0.002$ probability of getting a difference in sample means equal to the one observed in this study.

b. Assuming that the true mean road rage score is the same for males and females, there is a $0.002$ probability of getting a difference in sample means at least as large in either direction as the one observed in this study.

c. Assuming that the true mean road rage score is different for males and females, there is a $0.002$ probability of getting a difference in sample means at least as large in either direction as the one observed in this study.

d. Assuming that the true mean road rage score is the same for males and females, there is a $0.002$ probability that the null hypothesis is true.

e. Assuming that the true mean road rage score is the same for males and females, there is a $0.002$ probability that the alternative hypothesis is true.

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a. Construct and interpret a $95 %$ confidence interval for the difference in the true

proportion of U.S. men and U.S. women who can identify Egypt on a map.

b. Based on your interval, is there convincing evidence of a difference in the true

proportions of U.S. men and women who can identify Egypt on a map? Justify your

answer.

Cockroaches The pesticide diazinon is commonly used to treat infestations of the German cockroach, Blattella germanica. A study investigated the persistence of this pesticide on various types of surfaces. Researchers applied a $0.5 %$ emulsion of diazinon to glass and plasterboard. After $14$ days, they randomly assigned $72$ cockroaches to two groups of $36$ , placed one group on each surface, and recorded the number that died within $48$ hours. On glass, $18$ cockroaches died, while on plasterboard, $25$ died. If $p_{1}, p_{2}$

are the true proportions of cockroaches like these that would die within 48

hours on glass treated with diazinon and on plasterboard treated with diazinon,

respectively, check if the conditions for calculating a confidence interval for $p_{1} - p_{2}$ are met.

Quit smoking Nicotine patches are often used to help smokers quit. Does giving medicine to fight depression help? A randomized double-blind experiment assigned $244$ smokers to receive nicotine patches and another $245$ to receive both a patch and the antidepressant drug bupropion. After a year, $40$ subjects in the nicotine patch group had abstained from smoking, as had $87$ in the patch-plus-drug group. Construct and interpret a $99 %$ confidence interval for the difference in the true proportion of smokers like these who would abstain when using bupropion and a nicotine patch and the proportion who would abstain when using only a patch.

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