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.48 58 5161565974635350596060574663 57554755574361624967 55675549Use 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)UESTION 32(b) What is the upper bound (Round to 3 decimla places)

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Asked Nov 18, 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.
48 58 51
61
56
59
74
63
53
50
59
60
60
57
46
63 57
55
47
55
57
43
61
62
49
67 55
67
55
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)
UESTION 32
(b) What is the upper bound (Round to 3 decimla 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. 48 58 51 61 56 59 74 63 53 50 59 60 60 57 46 63 57 55 47 55 57 43 61 62 49 67 55 67 55 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) UESTION 32 (b) What is the upper bound (Round to 3 decimla places)

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Expert Answer

Step 1

The formula for 90% confidence interval for the mean age of CEO’s is given as

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CI tt

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Step 2

The sample mean and standard deviation can be obtained using Excel:

  • Enter the data into Excel file.
  • Enter “= AVERAGE (A1:A30)” to get the sample mean as 56.56
  • Enter “=STDEV.S (A1:A30)” to get the sample variance as 6. 90.
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That is 56.56,s=6.90 and n 30

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Step 3

The degrees of freedom corresponding to t distribution is n – 1.

That is, the degrees of freedom is, 29 (=30&ndas...

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