Question

The signed-rank test can be adapted for use in testing H0: μ = hypothesized value, where μ is the mean of a single population (see the last part of this section). Suppose that the time required to process a request at a bank’s automated teller machine is recorded for each of 10 randomly selected transactions, resulting in the following times (in minutes); 1.4, 2.1, 1.9, 1.7, 2.4, 2.9, 1.8, 1.9, 2.6, 2.2. Use the one-sample version of the signed-rank test and a .05 significance level to decide if the data indicate that the mean processing time exceeds 2 minutes.

Answer 1

Answer:

There is not enough evidence suggesting that the mean processing time exceeds 2 minutes.

Step-by-step explanation:

The hypothesis can be defined as follows:

H₀: The mean processing time is 2 minutes, i.e. μ = 2.

Hₐ: The mean processing time exceeds 2 minutes, i.e. μ > 2.

The significance level of the test is, α = 0.05.

Recorded Time (x)        (x - μ)          + Ranks             -Ranks

        1.4                          -0.6                                           8

        2.1                            0.1                   1

        1.9                           -0.1                                           1

        1.7                           -0.3                                          6

       2.4                            0.4                  7

       2.9                            0.9                10

       1.8                            -0.2                                          4

       1.9                            -0.1                                           1

       2.6                            0.6                 8

       2.2                            0.2                 4

    TOTAL                                              30                    20

Sum of +Ranks = 30

Sum of -Ranks = 20

Test statistic = Min (∑+Ranks, ∑-Ranks)

                     = Min (30, 20)

                     = 20

Compute the critical value using the Wilcoxon Signed-rank test table.

Critical value = 11

As the test statistic value is more than the critical value, the null hypothesis was failed to be rejected.

Thus, there is not enough evidence suggesting that the mean processing time exceeds 2 minutes.