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Chapter 10: Q. AP3.18 (page 703)

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.

Short Answer

Expert verified

The correct statement is:

b. About96% of the intervals constructed by this method will contain the true proportion of the labor force that is unemployed in the city.

Step by step solution

01

 Step 1: Given information 

We have to tell interval for the proportion of the labor force that is unemployed in a certain city.

02

Explanation 

The confidence intervals' upper and lower limits are made up of random variables and are therefore unpredictable. We fix the values and calculate the upper and lower bounds of the confidence interval once a sample has been gathered. Because they've already given you an interval, the answer is either yes or no as to whether the genuine population proportion falls within it. However, if we apply this procedure several times, we would find that approximately 96 percent of the intervals reflect the genuine proportion of unemployment in the city.

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Most popular questions from this chapter

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

A random sample of 200New York State voters included 88Republicans, while a random sample of 300California voters produced141Republicans. Which of the following represents the 95%confidence interval for the true difference in the proportion of Republicans in New York State and California?

a. (0.44โˆ’0.47)ยฑ1.96((0.44)(0.56)+(0.47)(0.53)200+300)

b. (0.44โˆ’0.47)ยฑ1.96((0.44)(0.56)200+(0.47)(0.53)300)

c. (0.44โˆ’0.47)ยฑ1.96(0.44)(0.56)200+(0.47)(0.53)300

d. (0.44โˆ’0.47)ยฑ1.96(0.44)(0.56)+(0.47)(0.53)200+300

e. (0.44โˆ’0.47)ยฑ1.96(0.45)(0.55)200+(0.45)(0.55)300

Which of the following is not a property of a binomial setting?

a. Outcomes of different trials are independent.

b. The chance process consists of a fixed number of trials, n.

c. The probability of success is the same for each trial.

d. Trials are repeated until a success occurs.

e. Each trial can result in either a success or a failure.

I want red!A candy maker offers Child and Adult bags of jelly beans with

different color mixes. The company claims that the Child mix has 30%red jelly beans, while the Adult mix contains 15%red jelly beans. Assume that the candy makerโ€™s claim is true. Suppose we take a random sample of 50jelly beans from the Child mix and a separate random sample of 100jelly beans from the Adult mix. Let p^Cand p^Abe the sample proportions of red jelly beans from the Child and

Adult mixes, respectively.

a. What is the shape of the sampling distribution of p^C-p^A? Why?

b. Find the mean of the sampling distribution.

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

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 โˆ’ 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.LetฮผA-B=3051526=0.200=20%ฮผAโˆ’B = the true mean difference (Variety A โˆ’ Variety B) in yield for tomato plants of these two varieties.

The P-value for a test of H0: ฮผAโˆ’B=03051526=0.200=20%versus Ha: ฮผAโˆ’Bโ‰ 0 is 0.227. Which of the following is the

correct interpretation of this P-value?

a. The probability that ฮผAโˆ’B is0.227.

b. Given that the true mean difference (Variety A โ€“ 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 โ€“ 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 โ€“ 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 โˆ’0.34is0.227.

e. Given that the true mean difference (Variety A โ€“ 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 โˆ’0.34is0.227.
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