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.

5	9	10	2	2	2	2	7	7	7	7	6	7
8	9	9	2	10	2	7	6	9	8	10	9	2
7	5	7	2	2	7	7	6	2	10	8	2	6
6	9	5	2	10	7	10	2	2	6	6

Develop a 95% confidence interval estimate of the population mean rating for Miami. Round your answers to two decimal places.

(____ , ____)

Answer 1

The mean of this data set is 6 while standard deviation is 2.86. Calculation is shown below:

A. D E G К L M 1 5 2. 2 2 2 7 10 7 7 б 7 2 8 2. 10 2 7 10 6 2 7 3 7 5 2 2 2 2 7 7 6 10 6 4 6 10 7 2. 2 10 2 6 6 6 =AVERAGE(A1:M4) Standard deviation STDEV.S(A1:M4) Mean 9 z NOn N N I CO CO

Below is the confidence interval formula:

S х —t- , х+t Vn п

here $\bar{x}$ is sample mean, s is sample standard deviation, n is the sample size and t is the 95% critical value of t/z distribution. We can take the value of t as 2.00.

95% confidence interval = [6 - 2*2.86/50^0.5 , 6 + 2*2.86/50^0.5]

= [6 - 0.81 , 6 +0.81]

= [5.19, 6.81]