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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 \(2. Based on last year’s book sales, we estimate that the standard deviation of the amount spent will be close to \)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×P×QE2

Z=1.645at confidence level =90%

=1.645×3022=609

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Most popular questions from this chapter

Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of 24laboratory rats. A 95%confidence interval for the mean blood cholesterol level μis 80.2to 89.8. Which of the following would cause the most worry about the validity of this interval?

a. There is a clear outlier in the data.

b. A stem plot of the data shows a mild right skew.

c. You do not know the population standard deviation σ.

d. The population distribution is not exactly Normal.

e. None of these are a problem when using a t interval.

California’s traffic People love living in California for many reasons, but traffic isn’t one of them. Based on a random sample of 572employed California adults, a 90%confidence interval for the average travel time to work for all employed California adults is 23minutes to 26 minutes.

a. Interpret the confidence level.

b. Name two things you could do to reduce the margin of error. What drawbacks do these actions have?

c. Describe how non response might lead to bias in this survey. Does the stated margin of error account for this possible bias?

Good wood? A lab supply company sells pieces of Douglas fir 4 inches long and

1.5 inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a distribution with standard deviation 3000 pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within 1000 pounds with 95% confidence. How large a sample is needed?

More prayer in school Refer to Exercise 5. Interpret the confidence level.

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whether they attended a religious service in the last 7 days. How large a sample would be required to obtain a margin of error of at most 0.01 in a 99% confidence interval for the population proportion who would say that they attended a religious service?
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