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 you want to be 99​% confident that the sample percentage is within 2.5 percentage points of the true population percentage. Complete parts​ (a) and​ (b) below.

a. Assume that nothing is known about the percentage of passengers who prefer aisle seats.

___ (Round up to the nearest​ integer.)

b. Assume that a prior survey suggests that about 31​% of air passengers prefer an aisle seat.

___(Round up to the nearest​ integer.)

Answer 1

Solution,

Given that,

a) = 1 - = 0.5   

margin of error = E = 0.025

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.576

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.576 / 0.025 )2 * 0.5 * 0.5

= 2654.31

sample size = n = 2655

b) = 0.31

1 - = 1 - 0.31 = 0.69

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.576 / 0.025 )2 * 0.31 * 0.69

= 2271.02

sample size = n = 2272