Question

The International Air Transport Association 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 for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.

Click on the datafile logo to reference the data.
6 4 6 8 7 7 6 3 3 8 10 4 8
7 8 7 5 9 5 8 4 3 8 5 5 4
4 4 8 4 5 6 2 5 9 9 8 4 8
9 9 5 9 7 8 3 10 8 9 6
Develop a 95% confidence interval estimate of the population mean rating for Miami. If required, round your answers to two decimal places. Do not round intermediate calculations.

Answer 1

The 95% confidence interval estimate of the population mean rating for Miami is (5.7, 7.0).

Explanation:

The (1 - α)% confidence interval for the population mean, when the population standard deviation is not provided is:

`CI=\bar x\pm t_(\alpha/2, (n-1))\cdot\ (s)/(√(n))`

The sample selected is of size, n = 50.

The critical value of t for 95% confidence level and (n - 1) = 49 degrees of freedom is:

`t_(\alpha/2, (n-1))=t_(0.05/2, 49)=2.000`

*Use a t-table.

Compute the sample mean and sample standard deviation as follows:

`\bar x=(1)/(n)\sum {x}=(1)/(50)* [6+4+6+...+9+6]=6.34\\\\s=\sqrt{(1)/(n-1)\sum (x-\bar x)^(2)}=\sqrt{(1)/(50-1)* 229.22}=2.163`

Compute the 95% confidence interval estimate of the population mean rating for Miami as follows:

`CI=\bar x\pm t_(\alpha/2, (n-1))\cdot\ (s)/(√(n))`

`=6.34\pm 2.00*(2.163)/(√(50))\\\\=6.34\pm 0.612\\\\=(5.728, 6.952)\\\\\approx(5.7, 7.0)`

Thus, the 95% confidence interval estimate of the population mean rating for Miami is (5.7, 7.0).