Question

6. A magazine published data on the best small firms in a certain year. 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 59 50 60 56
59 74 63 53 50
59 60 60 57 46
55 63 57 47 55
57 43 61 62 49
67 67 55 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. (Round your answers to two decimal places.)

Answer 1

$CI=\bar{X}\pm{t_{\alpha/2}}\frac{s}{\sqrt{n}}$

$t_{0.05, 29}=1.699$

$s=6.9269,n=30, \bar X=56.533$

$CI=56.533\pm1.699\frac{6.9269}{\sqrt{30}}$

$=56.533\pm2.1487$

$=(54.38,58.68)$