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Chapter 8: Q 23. (page 509)

The researcher is deciding between a 95% confidence level and a 99% confidence level. Compared with a 95% confidence interval, a 99% confidence interval will be

a. narrower and would involve a larger risk of being incorrect.

b. wider and would involve a smaller risk of being incorrect.

c. narrower and would involve a smaller risk of being incorrect.

d. wider and would involve a larger risk of being incorrect.

e. wider and would have the same risk of being incorrect.

Short Answer

Expert verified

Option (b) is correct.

Step by step solution

01

Given Information

Confidence intervals are95%,99%

02

Explanation

Width of confidence interval and confidence level are related positively.

If confidence level is high, degree of precision is higher, risk of being incorrect is lower.

For 99%confidence level, interval is wider and risk of being incorrect is lower.

Option (b) is correct.

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Most popular questions from this chapter

A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: “Do you think that the drinking age should be reduced to eighteen in light of the fact that 18-year-olds are eligible for military service?” He asks listeners to go to his website and vote “Yes” if they agree the drinking age should be lowered and “No” if not. Of the 100 people who voted, 70 answered “Yes.” Which of the following conditions are violated?

I. Random

II. 10%

III. Large Counts

a. I only

b. II only

c. III only

d. I and II only

e. I, II, and III

Batteries A company that produces AA batteries tests the lifetime of a randomsample of 30 batteries using a special device designed to imitate real-world use. Based onthe testing, the company makes the following statement: “Our AA batteries last an average of 430 to 470 minutes, and our confidence in that interval is 95%.”36

a. Determine the point estimate, margin of error, standard error, and sample standard

deviation.

b. A reporter translates the statistical announcement into “plain English” as follows: “95% of this company’s AA batteries last between 430 and 470 minutes.” Comment on this interpretation.

c. Your friend, who has just started studying statistics, claims that there is a 95% probability that the mean lifetime will fall between 430 and 470 minutes. Do you agree? Explain your reasoning.

d. Give a statistically correct interpretation of the confidence level that could be published in a newspaper report.

Explaining confidence The admissions director for a university found that (107.8,116.2)is a 95%confidence interval for the mean IQ score of all freshmen. Discuss whether each of the following explanations is correct, based on that information.

a. There is a 95%probability that the interval from role="math" localid="1654200953396" 107.8to116.2contains μ.

b. There is a 95%chance that the interval(107.8,116.2)contains x¯.

c. This interval was constructed using a method that produces intervals that capture the true mean in 95%of all possible samples.

d. If we take many samples, about 95%of them will contain the interval (107.8,116.2).

e. The probability that the interval (107.8,116.2)captures μ is either 0 or 1, but we don’t know which.

Reading scores in Atlanta The Trial Urban District Assessment (TUDA) is a

government-sponsored study of student achievement in large urban school districts. TUDA gives a reading test scored from 0to 500. A score of 243is a “basic” reading level and a score of 281is “proficient.” Scores for a random sample of 1470eighth-graders in Atlanta had a mean of 240with standard deviation of 42.17.

a. Construct and interpret a 99%confidence interval for the mean reading test score of all Atlanta eighth-graders.

b. Based on your interval from part (a), is there convincing evidence that the mean reading test score for all Atlanta eighth-graders is less than the basic level? Explain your answer.

More income The 2015American Community Survey estimated the median household income for each state. According to ACS, the 90%confidence interval for the 2015

median household income in New Jersey is \(72,222±\)610.

a. Interpret the confidence interval.

b. Interpret the confidence level.
See all solutions

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