[EX14-47] The following are 24 consecutive downtimes (in minutes) of a particular machine.

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 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.

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

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.