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Chapter 10: Q 7. (page 639)

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 14days, they randomly assigned 72cockroaches to two groups of 36, placed one group on each surface, and recorded the number that died within 48hours. On glass, 18cockroaches died, while on plasterboard, 25died. Ifp1,p2

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 p1-p2are met.

Short Answer

Expert verified

It is fit to find confidence interval,

Step by step solution

01

Given Information

It is given that n1=36

x1=18

n2=36

x2=25

02

Explanation

Conditions for hypothesis test are:

Random: As assigned arbitrarily, it is satisfied.

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

Normal: Success in first sample is 18and failures are 36-18=18, both are greater than ten, it is satisfied.

All conditions are fulfilled, we can calculate confidence interval forp1-p2

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Most popular questions from this chapter

A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of 60high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6hours with a standard deviation of 3hours. The researcher also obtained an independent SRS of 40high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 5hours with a standard deviation of 2hours. Suppose that the researcher decides to carry out a significance test of H0: μsuburban=μcity versus a two-sided alternativ

The P-value for the test is 0.048. A correct conclusion is to

a. fail to reject H0because0.048<α=0.05. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

b. fail to reject H0because 0.048<α=0.05. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

c. fail to reject H0because0.048<α=0.05. There is convincing evidence that the average time spent on extracurricular activities by students in the suburban and city school districts is the same.

d. reject H0because 0.048<α=0.05. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

e. reject H0because 0.048<α=0.05 . There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

Better barley Does drying barley seeds in a kiln increase the yield of barley? A famous experiment by William S. Gosset (who discovered the t distributions) investigated this question. Eleven pairs of adjacent plots were marked out in a large field. For each pair, regular barley seeds were planted in one plot and kiln-dried seeds were planted in the other. A coin flip was used to determine which plot in each pair got the regular barley seed and which got the kiln-dried seed. The following table displays the data on barley yield (pound per acre) for each plot.

Do these data provide convincing evidence at the α=0.05level that drying barley seeds in a kiln increases the yield of barley, on average?

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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.

Researchers suspect that Variety A tomato plants have a different average yield than Variety B tomato plants. To find out, researchers randomly select10Variety A and10Variety B tomato plants. Then the researchers divide in half each of10small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The10differences (Variety A − Variety B) in yield are recorded. A graph of the differences looks roughly symmetric and single-peaked with no outliers. The mean difference is x-=0.343051526=0.200=20%x-A-B=0.34and the standard deviation of the differences is s A-B=0.833051526=0.200=20%=sA-B=0.83.LetμA-B=3051526=0.200=20%μA−B = the true mean difference (Variety A − Variety B) in yield for tomato plants of these two varieties.

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b. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is0, the probability of getting a sample mean difference of0.34is0.227.

c. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is0, the probability of getting a sample mean difference of0.34or greater is0.227.

d. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is0, the probability of getting a sample mean difference greater than or equal to0.34or less than or equal to −0.34is0.227.

e. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is not 0, the probability of getting a sample mean difference greater than or equal to 0.34or less than or equal to −0.34is0.227.

A random sample of 100of last year’s model of a certain popular car found that 20had a specific minor defect in the brakes. The automaker adjusted the production process to try to reduce the proportion of cars with the brake problem. A random sample of 350of this year’s model found that 50had the minor brake defect.

a. Was the company’s adjustment successful? Carry out an appropriate test to support your answer. b. Based on your conclusion in part (a), which mistake—a Type I error or a Type II error—could have been made? Describe a possible consequence of this error.
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