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.
| 2 | 6 | 7 | 8 | 9 | 9 | 9 | 10 | 10 | 10 | 10 | 9 | 4 |
| 5 | 6 | 6 | 8 | 7 | 9 | 10 | 9 | 6 | 5 | 7 | 6 | 8 |
| 4 | 2 | 10 | 9 | 9 | 10 | 10 | 9 | 8 | 7 | 5 | 9 | 9 |
| 3 | 6 | 2 | 9 | 7 | 10 | 7 | 9 | 9 | 9 | 9 |
Develop a 95% confidence interval estimate of the population mean rating for Miami.
Σ(Xi - X̅ )2 = 262.48
Mean X̅ = Σ Xi / n
X̅ = 376 / 50 = 7.52
Sample Standard deviation SX = √ ( (Xi - X̅
)2 / n - 1 )
SX = √ ( 262.48 / 50 -1 ) = 2.3145
Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 50- 1 ) = 2.01 ( Critical value from t
table )
7.52 ± t(0.05/2, 50 -1) * 2.3145/√(50)
Lower Limit = 7.52 - t(0.05/2, 50 -1) 2.3145/√(50)
Lower Limit = 6.8621
Upper Limit = 7.52 + t(0.05/2, 50 -1) 2.3145/√(50)
Upper Limit = 8.1779
95% Confidence interval is ( 6.8621 , 8.1779 )
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