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Chapter 8: Q.110 (page 488)

Forbes magazine published data on the best small firms in 2012. These were firms that had been publicly traded for at least a year, have a stock price of at least \(5per share, and have reported annual revenue between \)5million and$1 billion.

The Table 8.13 shows the ages of the corporate CEOs for a random sample of these firms.

Use this sample data to construct a 90%confidence interval for the mean age of CEO鈥檚 for these top small firms. Use the Student's t-distribution.

Short Answer

Expert verified

We estimate that the average age of all CEOs of the greatest small businesses is between $54.421and$58.713 years, with a95% confidence level.

Step by step solution

01

Introduction

Create a 90%confidence interval for the average age of CEOs for these top small businesses using this sample data. The Student's-t distribution should be used.

02

Explanation 

Calculate the point estimate first.

x炉=56.567

Calculate the samples' standard deviations.

s=6.907,n=30,anddf=30-1=29

CL=0.90

伪=1-CL

=1-0.90=0.10a2=0.05ta2=t0.05=1.699

EBM=ta2sn

EBM=1.699690730

EBM=2.143

x炉-EBM=56.567-2.146

x炉-EBM=54.421

x炉+EBM=56.567+2.146

x炉+EBM=58.713

03

Result

We estimate that the average age of all CEOs of the greatest small businesses is between $54.421and$58.713 years, with a 95% confidence level.

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Most popular questions from this chapter

In six packages of 鈥淭he Flintstones庐 Real Fruit Snacks鈥� there were five Bam-Bam snack pieces. The total number of snack pieces in the six bags was 68.We wish to calculate a 96%confidence interval for the population proportion of Bam-Bam snack pieces.

a. Define the random variables XandP鈥�in words.

b. Which distribution should you use for this problem? Explain your choice

c. Calculatep鈥�.

d. Construct a 96%confidence interval for the population proportion of Bam-Bam snack pieces per bag.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. Do you think that six packages of fruit snacks yield enough data to give accurate results? Why or why not?

A poll of 1,200 voters asked what the most significant issue was in the upcoming election. Sixty-five percent answered the economy. We are interested in the population proportion of voters who feel the economy is the most important.

Define the random variable P鈥� in words.

Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in

the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly

surveyed 81people who recently served as jurors. The sample mean wait time was eight hours with a sample standard

deviation of four hours.

a.i.x虅=__________ii.sx=__________iii.n=__________iv.n鈥�1=__________

b. Define the random variables XandX虅in words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 95%confidence interval for the population mean time wasted.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. Explain in a complete sentence what the confidence interval means.

In complete sentences, explain why the confidence interval in Exercise 8.17 is larger than in Exercise 8.18.

The American Community Survey (ACS), part of the United States Census Bureau, conducts a yearly census similar to the one taken every ten years, but with a smaller percentage of participants. The most recent survey estimates with 90%confidence that the mean household income in the U.S. falls between \(69,720and\)69,922. Find the point estimate for mean U.S. household income and the error bound for mean U.S. household income.
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