Question

6. You have been given the task of estimating the percentage of southwest flights that arrive on time. How many flights must you survey in order to be 90% confident that your estimate is within three percentage points of the true population percentage? BE SURE TO SHOW YOUR WORK EVEN IF YOU ARE USING YOUR CALCULATOR.

Answer 1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 3% = 0.03

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= (1.645 / 0.03)2 * 0.5 * 0.5

= 751.54

= 752

n = sample size = 752