Question

You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you​ survey ? Assume that a prior survey suggests that about 73​% of air passengers prefer an aisle seat. Assume that you want to be 97% confident that the sample percentage is within 2.5 percentage points of the true population percentage.

Answer 1

This is a binomial experiment since either the passenger prefers aisle or doesn't.

Confidence interval

(1- )% CI for population proportion

    

Margin of error = Critical value * SE

= *  

So the margin of error tells us how much our sample proportion can increase or decrease to be within the confidence level. Here we want it to be within 2.5 percentage points

MOE = 2.5% = 0.025

Sample percentage = 73%  

(1- ) = 0.97 therefore = 0.03

Therefore the critical value at

=

= 2.1701 ..........using normal percentage table with p = 0.015

Now we have all the values we subsitute in MOE formula

0.025 = *

Squaring

The airport should survey 1485 passengers.