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 stockprice of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. The table below shows the ages of the corporateCEOS for a random sample of these firms.58 51 614856597463535059606057465563574755574361624967 55556749Use 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(a) what is the lower bound for 90% confidence interval for the mean age of CEO's? (Round to 3decimal places) (b) What is the upper bound (Round to 3 decimla places)

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Asked Nov 16, 2019
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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 $5 per share, and have reported annual revenue between $5 million and $1 billion. The table below shows the ages of the corporate
CEOS for a random sample of these firms.
58 51 61
48
56
59
74
63
53
50
59
60
60
57
46
55
635747
55
57
43
61
62
49
67 5555
67
49
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
(a) what is the lower bound for 90% confidence interval for the mean age of CEO's? (Round to 3decimal places)
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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 $5 per share, and have reported annual revenue between $5 million and $1 billion. The table below shows the ages of the corporate CEOS for a random sample of these firms. 58 51 61 48 56 59 74 63 53 50 59 60 60 57 46 55 635747 55 57 43 61 62 49 67 5555 67 49 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 (a) what is the lower bound for 90% confidence interval for the mean age of CEO's? (Round to 3decimal places)

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(b) What is the upper bound (Round to 3 decimla places)
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(b) What is the upper bound (Round to 3 decimla places)

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Expert Answer

Step 1

The mean is calculated using the Excel software. After entering the data in cells A1 to A30 (there are 30 observations), the formula =AVERAGE(A1:A30) gives the mean as 56.57 and standard deviation, the formula =STDEV(A1:A30) gives the standard deviation value...

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- et- =0.75 Vn Z0.05 P(z>Zoos)=0.05; P(z < -Z0.05)= 0.05 P(-00ssZ0os= 0.90 Zo.0s where Э )= 0.95. Thus, P(z Using EXCEL formula =NORM.SINV(0.95), Zoss 1.645. 0.05 Calculation 6.9 -,56.57 -1.645 V30 6.9 CI 56.57 -1.645-- 30 (54.49,58.64). Lower limit 54.49; Upper limit 58.64.

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