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Chapter 8: Q 16. (page 507)

How confident? The figure shows the result of taking 25SRSs from a Normal population and constructing a confidence interval for the population mean using each sample. Which confidence level—80%,90%,95%,or99%—do you think was used? Explain your reasoning.

Short Answer

Expert verified

Confidence Level of99%is used.

Step by step solution

01

Given Information

We are given that

02

Determining Confidence Level Used

Confidence Level is calculated as 2525=1

100%

  • Red line implies those sample means which have no true population mean.
  • There are zero samples among given 25samples not containing true proportion.
  • Hence, 25samples from 25samples has true population.
  • The confidence level which is closest is99%

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Most popular questions from this chapter

Selling online According to a recent Pew Research Center report, many

American adults have made money by selling something online. In a random sample of 4579American adults, 914reported that they earned money by selling something online in the previous year. Assume the conditions for inference are met.

Determine the critical value z* for a 98% confidence interval for a proportion.

b. Construct a 98% confidence interval for the proportion of all American adults who

would report having earned money by selling something online in the previous year.

c. Interpret the interval from part (b).

Losing weight A Gallup poll asked a random sample of U.S. adults, “Would you like to lose weight?” Based on this poll, the 95%confidence interval for the population

proportion who want to lose weight is (0.56,0.62).

a. Interpret the confidence interval.

b. What is the point estimate that was used to create the interval? What is the margin of error?

c. Based on this poll, Gallup claims that more than half of U.S. adults want to lose weight. Use the confidence interval to evaluate this claim.

10Bottling cola A particular type of diet cola advertises that each can contains 12 ounces of the beverage. Each hour, a supervisor selects cans at random, measures their contents, and computes a 95%confidence interval for the true mean volume. For one particular hour, the 95%confidence interval is 11.97ounces to 12.05ounces.

a. Does the confidence interval provide convincing evidence that the true mean volume is different than 12ounces? Explain your answer.

b. Does the confidence interval provide convincing evidence that the true mean volume is 12ounces? Explain your answer.

Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172172undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?” Only 19answered “Yes.” Assume the conditions for inference are met.

a. Determine the critical valueZ*for a 96%confidence interval for a proportion.

b. Construct a 96%confidence interval for the proportion of all undergraduates at this university who would go to the professor.

c. Interpret the interval from part (b).

The 10%condition When constructing a confidence interval for a population proportion, we check that the sample size is less than 10%of the population size.

a. Why is it necessary to check this condition?

b. What happens to the capture rate if this condition is violated?
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