Question

The International Air Transport Association survey's business travelers to develop quality rating for transatlantic gateways airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each travelers is ask to provide a rating for the Miami International Airport . The rating obtained from the sample of 50 business travelers follow :


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.

Answer 1

Mean value:

$$X = \frac {\sum_ {i = 1} ^ {N} x _ {i}}{N} = 6. 3 4$$

Standard deviation:

$$\sigma (r) = \sqrt {\frac {1}{N - 1} \sum_ {i = 1} ^ {N} (x _ {i} - r) ^ {2}}.$$

$\mathbf{r} = \mathbf{X}$ - mean value.

$\sigma = 2.16$

95% confidence interval estimate is $1.96\sigma = 2.16^{*}1.96 = 4.23$

Answer: 4.23