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 3.5 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. nequals b. Assume that a prior survey suggests that about 33​% of air passengers prefer an aisle seat n=___

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 3.5% = 0.035

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z_/2 = 2.576 ( Using z table )

Sample size = n = (Z_/2 / E)² * * (1 - )

= (2.576 / 0.035)² * 0.5 * 0.5

=1354.24

Sample size = 1355

(B)

Solution :

Given that,

= 0.33

1 - = 1 - 0.33 = 0.67

margin of error = E = 3.5% = 0.035

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z_/2 = 2.576 ( Using z table )

Sample size = n = (Z_/2 / E)² * * (1 - )

= (2.576 / 0.035)² * 0.33 * 0.67

=1197.69

Sample size = 1198