Question

In Exercises 1–4, use the following listed arrival delay times (minutes) for American Airline flights from New York to Los Angeles. Negative values correspond to flights that arrived early. Also shown are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different flights have the same mean arrival delay time.

Flight 1	-32	-25	-26	-6	5	-15	-17	-36
Flight 19	-5	-32	-13	-9	-19	49	-30	-23
Flight 21	-23	28	103	-19	-5	-46	13	-3

P-Value If we use a 0.05 significance level in analysis of variance with the sample data given in Exercise 1, what is the P-value? What should we conclude? If a passenger abhors late flight arrivals, can that passenger be helped by selecting one of the flights?

Short answer

The p-value for the test is 0.285.

The null hypothesis is failed to be rejected at 0.05 level of significance.

The passenger cannot be helped as all flights have statistically the same mean arrival delay time.

Step-by-step solution

Given information

The SPSS output for the arrival delay times, along with the observations of three flights,are given.

Identify the p-value

P-value is the probability of obtaininga value as extreme as the test statistic. If the value is large, the chances of rejecting the null hypothesis lower.

From the output table, the value computed in the significance column against the test statistic is the p-value,which is 0.285.

Decision rule using the p-value

The decision rule states two criteria:

• If the p-value is greater than the significance level, the null hypothesis fails to be rejected.
• If the p-value is lower than the significance level, the null hypothesis is rejected.

The significance level is 0.05. The p-value is larger than 0.05, implying that the null hypothesis would fail to be rejected at a 0.05 level of significance.

The statistical hypothesis for the test is as follows:

Null hypothesis: The mean of arrival delays for all flights is the same.

Alternative hypothesis: The mean of arrival delays for at least one flight differs.

As a result, it can be stated that there is sufficient evidence to conclude that the mean arrival delay for all flights is equal.

Explain if one of the flights can be selected

As per the conclusion, the mean arrival delay for all three flights is equal. Thus, no flight is different from the rest based on the arrival delay time.

Thus, it is difficult to help the passenger select one of these flights.