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

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 6.76

S = 2.55199002

n = 50

df = n – 1 = 49

Confidence level = 95%

Critical t value = 2.0096

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 6.76 ± 2.0096*2.55199002/sqrt(50)

Confidence interval = 6.76 ± 2.0096*0.36090589

Confidence interval = 6.76 ± 0.7253

Lower limit = 6.76 - 0.7253 = 6.03

Upper limit = 6.76 + 0.7253 = 7.49

Confidence interval = (6.03, 7.49)