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= 3007

b. Assume that a prior survey suggests that about 38% of air passengers prefer an aisle seat.

n= ?

Answer 1

Answer: 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.

Solution:

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

Assume, p = 0.50

At 90% confidence interval,

Zα/2 = 1.645

Margin of error E = 1.5% = 0.015

Sample size n:

n = p(1-p) * (Zα/2 / E)^2

n = 0.5(1-0.5) * (1.645 /0.015)^2

n = 3006.69

n = 3007

Therefore, required air passengers are 3007.

b. Assume that a prior survey suggests that about 38% of air passengers prefer an aisle seat.

p = 38% = 0.38

Sample size n:

n = p(1-p) * (Zα/2 / E)^2

n = 0.38(1-0.38) * (1.645 /0.015)^2

n = 2833.5088

n = 2834

Therefore, required air passengers are 2834.