Question

A study was conducted on the percentages of on-time arrivals for major U.S. airlines. Two regional airlines were surveyed. For Airline A, 213 out of 300 flights were on-time. For Airline B, 185 out of 250 were on-time. Construct a 90% confidence interval for the difference between the proportions of flights that are on-time for Airline A and Airline B.

options:

-0.128 < p1 - p2 < 0.068

-0.119 < p1 - p2 < 0.059

-0.093 < p1 - p2 < 0.033

-0.079 < p1 - p2 < 0.019

-0.105 < p1 - p2 < 0.045

Answer 1

Confidence interval for the difference between the proportions

for 90% confidence level =(100-90)/100=0.10

/2 = 0.10/2=0.05

Z/2=Z0.05=1.6449

For Airline A Sample

Number of flights :n1=300

Number of flights on time :x1=213

Sample proportion of flights on time for Airline A Sample : = 213/300 = 0.71

For Airline B sample

Number of flights :n2=185

Number of flights on time :x2=250

Sample proportion of flights on time for Airline B Sample : = 185/250=0.74

90% confidence interval for the difference between the proportions of flights that are on-time for Airline A and Airline B

90% confidence interval for the difference between the proportions of flights that are on-time for Airline A and Airline B

-0.093 <p1-p2<0.033

Answer :

-0.093 < p1 - p2 < 0.033