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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 a recent sample of 84used car sales costs, the sample mean was \(6,425with a standard deviation of \)3,156. Assume

the underlying distribution is approximately normal.

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

b. Define the random variableXin words.

c. Construct a 95%confidence interval for the population mean cost of a used car.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

d. Explain what a 鈥�95% confidence interval鈥� means for this study.

Suppose that 14children, who were learning to ride two-wheel bikes, were surveyed to determine how long they had

to use training wheels. It was revealed that they used them an average of six months with a sample standard deviation of

three months. Assume that the underlying population distribution is normal.

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

b. Define the random variable Xin words.

c. Define the random variable Xin words.

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

e. Construct a 99%confidence interval for the population mean length of time using training wheels.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

f. Why would the error bound change if the confidence level were lowered to 90%?

Define the random variablesX andx{"x":[[179,180,181,183,186,189,193,196,198,200,202,204,205,207,208,210,211,212,213,214,214,215,215,215,215,215,215,214,212,211,209,207,206,204,203,201,199,198,197,195,194,193,192,191],[226,225,224,221,219,218,217,215,214,213,213,212,212,211,211,211,211,211,211,212,213,214,216,217,220,223,225,227,229,232,233,235,236,238,239,240,241,242,242,243],[164,165,168,176,181,187,192,197,202,205,207,212,215,216,218,219,220,221,222]],"y":[[101,100,100,99,97,96,96,96,96,96,96,97,98,100,100,102,104,105,107,108,109,111,112,113,115,117,119,121,123,124,125,127,127,128,128,129,129,129,129,129,129,129,128,128],[88,89,90,93,95,97,98,100,101,103,104,104,105,107,108,109,110,111,113,114,114,115,116,118,119,120,121,121,121,121,121,121,121,121,120,120,120,120,119,119],[84,84,83,81,80,78,77,77,76,76,75,75,74,73,73,73,72,72,72]],"t":[[0,334,339,357,374,390,408,424,440,457,473,490,506,523,540,557,574,590,606,623,640,657,675,689,706,724,740,756,774,789,806,823,840,857,873,890,907,923,940,957,974,990,1006,1023],[2075,2299,2306,2324,2340,2356,2373,2389,2406,2423,2443,2458,2473,2490,2508,2523,2551,2590,2606,2623,2640,2656,2674,2690,2707,2723,2740,2756,2772,2789,2806,2823,2840,2856,2873,2890,2907,2956,2973,2989],[4121,4332,4340,4356,4373,4389,4406,4423,4440,4456,4473,4489,4506,4523,4539,4557,4573,4598,4656]],"version":"2.0.0"} in words.

Using the same mean, standard deviation, and level of confidence, suppose that n were 69 instead of 25. Would the error bound become larger or smaller? How do you know?

The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X=the age of a Winter Foothill College student.

In words, define the random variable X炉.
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