Question

1. The following data on flight delays for United and Southwest is provided:
   1. What is the 98% confidence interval for the difference in flight delays from United to Southwest?
   2. What is the test statistic for testing to see if there is a significant difference in the number of delays?

Airline	United	Southwest
Sample Size	40	42
Average Number of Delays per Month	141	361
Population Standard Deviation	270	402

Answer 1

(A) Population standard deviations are known and sample sizes are big enough, so we will use z distribution

formula for the confidence interval of mean difference is given as

setting the values from the question and z score for 98% confidence interval is 2.33 (using distribution critical value table)

we get

this gives us

So, 98% confidence interval for the mean difference is (-395.451,-44.549)

(B) Since population standard deviations are known and sample sizes are big enough, so we will use z distribution. So, a two-Sample z-test for Comparing two means is best suited for testing the hypothesis

Formula for z test statistic is given as

setting the given values, we get

on solving, we get

z =-220/75.30 = -2.92

So, required test statistic is z= -2.92