Question

The mean number of flight hours for Continental Airline pilots is 49 hours per month. Assume that this mean was based on a sample of 100 Continental pilots and that the sample standard deviation was 11.5 hours. Calculate the margin of error for a 95% confidence interval.

Answer 1

The margin of error for a 95% confidence interval is of 2.18 hours.

Explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 100 - 1 = 99

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 99 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.95)/(2) = 0.975`. So we have T = 1.984

The margin of error is:

`M = T(s)/(√(n))`

In which s is the standard deviation of the sample(square root of the variance) and n is the size of the sample.

In this question:

`s = 11.5, n = 100`. So

`M = T(s)/(√(n))`

`M = 1.984(11)/(√(100))`

`M = 2.18`

The margin of error for a 95% confidence interval is of 2.18 hours.