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 90​%confident that the sample percentage is within 1.5 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. n=

b. Assume that a prior survey suggests that about 32​% of air passengers prefer an aisle seat. n=

Answer 1

Solution :

Given that,

margin of error = E = 0.015

Z_/2 = 1.645

(a)

= 0.5

1 - = 0.5

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

= (1.645 / 0.015)² * 0.5 * 0.5

= 3007

sample size = n = 3007

(b)

= 0.32

1 - = 0.68

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

= (1.645 / 0.015)² * 0.32 * 0.68

= 2617.03

sample size = n = 2617