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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

Music and memory Does listening to music while studying help or hinder students鈥� learning? Two statistics students designed an experiment to find out. They selected a random sample of 30students from their medium-sized high school to participate. Each subject was given 10minutes to memorize two different lists of 20words, once while listening to music and once in silence. The order of the two word lists was determined at random; so was the order of the treatments. The difference (Silence 鈭� Music) in the number of words recalled was recorded for each subject. The mean difference was 1.57and the standard deviation of the differences was 2.70.

a. If the result of this study is statistically significant, can you conclude that the difference in the ability to memorize words was caused by whether students were performing the task in silence or with music playing? Why or why not?

b. Do the data provide convincing evidence at the伪=0.01 significance level that the number of words recalled in silence or when listening to music differs, on average, for students at this school?

c. Based on your conclusion in part (a), which type of error鈥攁 Type I error or a Type II error鈥攃ould you have made? Explain your answer.

A 96% confidence interval for the proportion of the labor force that is unemployed in a certain city is (0.07,0.10). Which of the following statements is true?

a. The probability is 0.96 that between 7%and10% of the labor force is unemployed.

b. About 96% of the intervals constructed by this method will contain the true proportion of the labor force that is unemployed in the city.

c. In repeated samples of the same size, there is a 96% chance that the sample proportion will fall between 0.07and0.10.

d. The true rate of unemployment in the labor force lies within this interval 96% of the time.

e. Between 7%and10%of the labor force is unemployed 96% of the time.

According to sleep researchers, if you are between the ages of 12and 18years old, you need 9 hours of sleep to function well. A simple random sample of 28students was chosen from a large high school, and these students were asked how much sleep they got the previous night. The mean of the responses was 7.9hours with a standard deviation of 2.1hours.

Which of the following is the standardized test statistic for the hypothesis test ?

  1. localid="1654221307488" t=7.9-92.128andt=7.9-92.128
  2. t=9-7.92.128andt=9-7.92.128
  3. t=7.9-92.128and t=7.9-92.128
  4. localid="1654221494579" t=7.9-92.127andt=7.9-92.127
  5. localid="1654221497857" t=9-7.92.127andt=9-7.92.127

Bird eggs A researcher wants to see if birds that build larger nests lay larger eggs. She selects two random samples of nests: one of the small nests and the other of large nests. Then she weighs one egg (chosen at random if there is more than one egg) from each nest. A 95% confidence interval for the difference (Large 鈭� Small) between the mean mass (in

grams) of eggs in small and large nests is 1.6卤2.0 role="math" localid="1654714720708" 3051526=0.200=20.0%1.6卤2.0

a. Does the interval provide convincing evidence of a difference in the true mean egg mass of birds with small nests and birds with large nests? Explain your answer.

b. Does the interval provide convincing evidence that the true mean egg mass of birds with small nests and birds with large nests is the same? Explain your answer.

American-made cars Nathan and Kyle both work for the Department of Motor Vehicles (DMV), but they live in different states. In Nathan鈥檚 state, 80%of the registered cars are made by American manufacturers. In Kyle鈥檚 state, only 60%of the registered cars are made by American manufacturers. Nathan selects a random sample of 100cars in his state and Kyle selects a random sample of 70cars in his state. Let pn-pkbe the difference (Nathan鈥檚 state 鈥� Kyle鈥檚 state) in the sample proportion of cars made by American manufacturers.

a. What is the shape of the sampling distribution of pn-pk? Why?

b. Find the mean of the sampling distribution.

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

See all solutions

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