Before a merger with Republic Airlines, Northwest Airlines took a SRS of 100 fli

Question

Before a merger with Republic Airlines, Northwest Airlines took a SRS of 100 flights and found that 86 of them departed on time. After the merger, they took a SRS of 100 flights and found that 65 of them departed on time. Airline mergers tend to cause an increase in flight delays, and the sample evidence seems to support this. Perform a formal hypothesis test at the 5% level of significance to see if there is sufficient evidence to support the claim that the proportion of on-time departures were higher prior to the merger.

Explanation / Answer

Let p1 be the proportion of flights departures on time before merger.

Let p2 be the proportion of flights departures on time after merger.

we solve this problem by testing two proportion test

Here we want to test that

So null hypothesis is H0 : P1 < P2 that is the proportion of on-time departures were higher than before merger.

and alternative hypothesis is H1 : P1 > P2

We can used two sample proportion z test.

level of significance = 0.05

Using minitab.

The command for two sample proportion z test in minitab is

Choose Stat > Basic Statistics > 2 Proportions.

Choose Summarized data.

In First sample, under Events, enter . Under Trials, enter .

In Second sample, under Events, enter . Under Trials, enter .

Click on "Option"

Level of confidence in percentage = c = ( 1- lpha)*100 = = (1 -0.05)*100 = 95.0

so put "Confidence level " = 95.0

Test Difference

Alternative = Greater than

Then click on OK and again click on OK

So we get the following output

MTB > PTwo 100 86 100 65;
SUBC>   Alternative 1.

Test and CI for Two Proportions

Sample   X    N    Sample p
    1       86 100     0.860000
    2       65 100     0.650000

Difference = p (1) - p (2)
Estimate for difference: 0.21
95% lower bound for difference: 0.112982

Test for difference = 0 (vs > 0): Z = 3.56 P-Value = 0.000

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0 < 0.05 so we used first rule.

That is we reject null hypothesis

Conclusion: At 5% level of significance there are not sufficient evidence to say that the proportion of on-time departures were higher than before merger.

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