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Chapter 8: Q. 21 (page 483)

A researcher plans to use a random sample of n=500families to estimate the mean monthly family income for a large population. A99%confidence interval based on the sample would be ______ than a 90% confidence interval.

(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, but it cannot be determined whether the risk of being incorrect would be larger or smaller

Short Answer

Expert verified

(b) wider and would involve a smaller risk of being incorrect

Step by step solution

01

Given Information

(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, but it cannot be determined whether the risk of being incorrect would be larger or smaller

02

Explanation

A 99%confidence interval will be wider than a 90%confidence interval because a 99%confidence interval will result in an interval that is more likely to contain the true population mean than the90% confidence interval.

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Most popular questions from this chapter

The AP Statistics class in Exercise 1 also asked an SRS of 20 boys at their school how many shoes they have. A 95% confidence interval for the difference in the population means (girls 鈥� boys) is 10.9 to 26.5. Interpret the confidence interval and the confidence level.

NAEP scores Refer to Exercise 5. Below your sketch, choose one value of x inside the shaded region and draw its corresponding confidence interval. Do the same for one value of x outside the shaded region. What is the most important difference between these intervals?

18. Explaining confidence The admissions director from Big City University found that (107.8, 116.2) is a 95% confidence interval for the mean IQ score of all freshmen. Comment on whether or not each of the following explanations is correct.
(a) There is a 95%probability that the interval from 107.8to 116.2contains 渭.
(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) 95%of all possible samples will contain the interval (107.8,116.2).

(e) The probability that the interval (107.8,116.2)captures 渭is either 0or 1, but we don鈥檛 know which.

Gambling and the NCAA Gambling is an issue of great concern to those involved in college athletics. Because of this concern, the National Collegiate Athletic Association (NCAA) surveyed randomly selected student-athletes concerning their gambling-related behaviors.17Of the 5594Division I male athletes in the survey, 3547reported participation in some gambling behavior. This includes playing cards, betting on games of skill, buying lottery tickets, betting on sports, and similar activities. A report of this study cited a 1% margin of error.

(a) The con铿乨ence level was not stated in the report. Use what you have learned to 铿乶d the con铿乨ence level, assuming that the NCAA took an SRS.

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A milk processor monitors the number of bacteria per millilitre in raw milk received at the factory. A random sample of 10 one-millilitre specimens of milk supplied by one producer gives the following data:

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Construct and interpret a 90% confidence interval for the population mean 渭.
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