Question

Exercise 08.17 Algorith mie Check My Work The International Air Transport Assodiation surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating far the Miami International Airpart. The ratings obtained from the sample of 50 business travelers follaw 10 109 3 10 8 10 4 73 10 10 Davelop 95% confidence interval estimate of the population mean rating for Miami. Round your answers to two decimal places. Hide Feedback Incorrect Chock My Wark

Answer 1

$\textup{Sample size, n} = 50$

_{$\textup{Sample Mean, }\bar x=\Sigma x/ n = 398/50 = \textbf{7.96}$}

$\textup{Sample standard deviation, s = }\sqrt{\frac{\Sigma(x-\bar x)^2}{n-1}}$

$=\sqrt{\frac{(3-7.96)^2+(6-7.96)^2+.....+(8-7.96)^2}{50-1}} = \textbf{1.895}$

$\textup{At }\alpha \textup{= 0.05 and df = 50-1=49 critical value, }t_{\alpha /2} = 2.01$

$\textup{95\% confidence interval for the population mean}$

$\left ( \bar x \pm t_{\alpha /2}*\frac{s}{\sqrt{n}} \right )$

$\left ( 7.96 \pm 2.01*\frac{1.895}{\sqrt{50}} \right )$

$(\textbf{7.42, 8.50})$