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 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 business travelers follow. 1 5 6 7 8 8 8 9 9 9 9 10 3 4 5 5 7 6 8 9 10 5 4 6 5 7 3 1 9 8 8 9 9 10 7 6 4 8 10 2 5 1 8 6 9 6 8 8 10 10 Develop a confidence interval estimate of the population mean rating for Miami. Round your answers to two decimal places.

The 95% confidence interval would be given by (6.03;7.49)    

Step-by-step explanation:

Notation

represent the sample mean

population mean (variable of interest)

s represent the sample standard deviation

n=50 represent the sample size  

Solution

The confidence interval for the mean is given by the following formula:

  (1)

We can calculate the mean and the sample deviation we can use the following formulas:  

(2)  

(3)  

The mean calculated for this case is

The sample deviation calculated

In order to calculate the critical value we need to find first the degrees of freedom, given by:

We assume a standard confidence level of 0.95 or 95%, the value of and , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that

Now we have everything in order to replace into formula (1):

The 95% confidence interval would be given by (6.03;7.49)