Question

State wheter you think the differents between what occurred and what you would expect by chance is statistically significant

an airline with a 95% on- time departure rate has 11 out of 200 flights with late depatures

Answer 1

It is given that 11 out of 200 flights are with late departures.

Then in order to find the 95% confidence interval we will use binomial proportion

here x = 11

n = 200

So 95% CI is given by:

where

and

is the critical value of standard normal distribution.

substituting values in the above equation we get CI

which suggests that if we draw 100 samples then 95 samples out of them have proportion between above given interval.

i.e., is the 95% confident that proportion of late departures lies in this interval.