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Chapter 8: Q.8 (page 524)

Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of \(2. Based on last year鈥檚 book sales, we estimate that the standard deviation of the amount spent will be close to \)30. The number of observations required is closest to

(a) 25. (b) 30. (c) 608. (d) 609. (e) 865.

Short Answer

Expert verified

The number of observations required is the closest to609.

Step by step solution

01

introduction

We know, confidence level = 90%

Interval is to have a margin of error E=2

The standard deviation of the amount spent will be P =30

02

explanation

Calculating the sample size S=Z2脳P脳QE2

Z=1.645at confidence level =90%

=1.645脳3022=609

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Most popular questions from this chapter

A school of fish Refer to Exercise 74.

a. Explain why it was necessary to inspect a graph of the sample data when checking the Normal/Large Sample condition.

b. According to the packaging, there are supposed to be 330goldfish in each bag of crackers. Based on the interval, is there convincing evidence that the average number of goldfish is less than 330? Explain your answer.

After deciding on a 95% confidence level, the researcher is deciding between a sample of size n=500 and a sample of size n=1000. Compared with using a sample size of n=500, a confidence interval based on a sample size of n=1000 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. narrower and would have the same risk of being incorrect.

More online sales Refer to Exercise 35. Calculate and interpret the standard error ofp^=xn for these data.

It鈥檚 critical Find the appropriate critical value for constructing a confidence interval in each of the following settings.

a. Estimating a population proportion p at a 94% confidence level based on an SRS of size 125

b. Estimating a population mean 渭 at a 99% confidence level based on an SRS of size 58

Three branches According to a recent study by the Annenberg Foundation, only 36%of adults in the United States could name all three branches of government. This was based on a survey given to a random sample of1416U.S. adults.

a. Construct and interpret a 90%confidence interval for the proportion of all U.S. adults who could name all three branches of government.

b. Does the interval from part (a) provide convincing evidence that less than half of all U.S. adults could name all three branches of government? Explain your answer.
See all solutions

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