Question

When flights are delayed, do two of the worst airports experience delays of the same length? Suppose the delay times in minutes for seven recent, randomly selected delayed flights departing from each of these airports are as follows.

Airport 1	Airport 2
63	104
96	34
48	32
31	85
52	79
24	41
46	55

Use the MWW test to determine if there is a difference in length of flight delays for these two airports. Use α = 0.05.

State the null and alternative hypotheses.

H₀: The two populations of flight delays are identical.
H_a: The two populations of flight delays are not identical.H₀: The two populations of flight delays are not identical.
H_a: The two populations of flight delays are identical.    H₀: Median delay time for airport 1 − Median delay time for airport 2 ≤ 0
H_a: Median delay time for airport 1 − Median delay time for airport 2 > 0H₀: Median delay time for airport 1 − Median delay time for airport 2 < 0
H_a: Median delay time for airport 1 − Median delay time for airport 2 = 0H₀: Median delay time for airport 1 − Median delay time for airport 2 ≥ 0
H_a: Median delay time for airport 1 − Median delay time for airport 2 < 0

Find the value of the test statistic.

W =

What is the p-value? (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Reject H₀. There is sufficient evidence to conclude that there is a significant difference in length of flight delays for these two airports.Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference in length of flight delays for these two airports.    Reject H₀. There is not sufficient evidence to conclude that there is a significant difference in length of flight delays for these two airports.Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference in length of flight delays for these two airports.

Answer 1

The Mann-Whitney U test is a non-parametric test that can be used to test the null hypothesis that two samples come from the same population (i.e. have the same median) or, alternatively, whether observations in one sample tend to be larger than observations in the other.

We use minitab to perform the non parametric test.

1. The correct null and alternative hypothesis is

H₀: The two populations of flight delays are identical.
H_a: The two populations of flight delays are not identical

2. steps in minitab to perform the test : stat,non parametric, Mann-Whitney

Output :

2. value of the test statistic.

W =47 (from above output)

3. p-value = 0.5229

4. CONCLUSION : As p-value=0.5229>0.05=alpha , we accept H0 i.e .Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference in length of flight delays for these two airports.