This part of the question concerns data on the lengths of the 51 time intervals (in days) between successive earthquakes in California, starting from a major earthquake on 9 January 1857, up to an earthquake on 24 August 2014. (To qualify for inclusion in this dataset, earthquakes had to be single mainshocks with magnitude at least 4.9.) These time intervals are in the variable Interval in the worksheet california-earthquakes.mwx. In this part of the question, you will explore whether or not a Poisson process is a suitable model for these data

(i) The intervals between successive events in a Poisson process are exponentially distributed. Using Minitab, find the mean and standard deviation of the intervals between earthquakes in California. Are these values consistent with the data being observations from an exponential distribution? Give a reason for your answer.

(ii) Using Minitab, obtain a histogram with the following properties:

the ticks on the horizontal axis are at the cutpoints

the bins have width 500 days

the first bin starts at 0 days and the last bin finishes at 7500 days.

Include a copy of your histogram in your answer. Is the shape of the histogram consistent with the data being observations from an exponential distribution? Give a reason for your answer.

(iii) The data are listed in the order in which they arose. Using Minitab, produce an appropriate graph to investigate whether, for the period of observation, the data are consistent with the rate at which earthquakes occur in California remaining constant. Include a copy of your graph in your answer. Explain why your graph suggests that the average rate at which earthquakes occurred in California was not constant over the period. How did the average rate change over time?

california-earthquakes.mwx

Interval

3194

1109

1252

7273

56

2806

2305

3352

1034

792

945

889

858

1676

277

2626

3122

1325

32

851

822

4035

541

496

2742

358

70

101

122

167

905

358

805

13

437

53

624

70

619

299

3

64

568

2098

323

1205

1408

273

529

85

1603