Using Nonparametric Tests. In Exercises 1–10, use a 0.05 significance level with the indicated test. If no particular test is specified, use the appropriate nonparametric test from this chapter.

Airline Fares Refer to the same data from the preceding exercise. Use the Wilcoxon signed ranks test to test the claim that differences between fares for flights scheduled 1 day in advance and those scheduled 30 days in advance have a median equal to 0. What do the results suggest?

Twosamples show the airfares of eight different flights from New York to San Francisco.

It is claimed that the differences between the fares of flights scheduled oneday in advance and those scheduled 30 days in advance have a median equal to 0.

The Wilcoxon signed-ranks test is used to test the claim that there is no difference in the cost between the flights scheduled oneday prior and the flights scheduled 30 days prior.

The null hypothesis is as follows:

The difference between the costs of flights scheduled oneday in advance and those scheduled 30 days in advance have a median equal to 0.

The alternative hypothesis is as follows:

The difference between the costs of flights scheduled oneday in advance and those scheduled 30 days in advance does not have a median equal to 0.

If the value of the test statistic is less than the critical value, the null hypothesis is rejected, else not.

Compute the differences of the values by subtracting the cost of the flights scheduled 30 days prior from the cost of thosescheduled oneday prior.

Compute the ranks of the absolute differences by assigning rank 1 to the smallest difference, rank 2 to the next smallest difference, and so on.

Mark the sign of the ranks corresponding to the sign of the difference.

The following table shows the signedranks:

The total number of observations (n) is 8.

Since \(n < 30\), the value of the test statistic (T) needs to be determined.

Compute the sum of the positive ranks as shown:

\(\begin{array}{c}Su{m_{positive}} = 5 + 2 + .... + 8\\ = 36\end{array}\)

Since there are no negative ranks, \(Su{m_{negative}} = 0\).

T assumes a value corresponding to the smaller of the two sums.

Thus, \(T = 0\).

The critical value of T for n=8 and \(\alpha = 0.05\) for a two-tailed test is equal to 4.

Since the value of the test statistic is less than the critical value, the null hypothesis is rejected.

There is enough evidence to conclude that the difference between the costs of flights scheduled one day in advance and those scheduled 30 days in advance does not have a median equal to 0.