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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’s 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¯=56.567

Calculate the samples' standard deviations.

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

CL=0.90

α=1-CL

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

EBM=ta2sn

EBM=1.699690730

EBM=2.143

x¯-EBM=56.567-2.146

x¯-EBM=54.421

x¯+EBM=56.567+2.146

x¯+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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