The following are 24 consecutive downtimes (in minutes) of a particular machine.

The null hypothesis of randomness is to be tested against the alternative that there is a trend. A MINITAB analysis of the number of runs above and below the median follows.

a. Confirm the values reported for the median and the number of runs by calculating them yourself.
b. Compute the value of z_ and the p-value.
c. Would you reject the hypothesis of randomness? Explain.
d. Construct a graph that displays the sample data and visually supports your answer to part c.

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Downtime 20 33 33 35 36 36 22 22 25 27 30 30 30 31 31 32 32 36 40 40 50 45 45 40 2 2 2 2 2 2 5 2 2 Runs Test: Downtime Runs test for Downtime Runs above and below K 32.5 The observed number of runs 4 The expected number of runs 13.0000 12 Observations above K 12 below The test is significant at 0.0002