Question

Researchers experimenting with cloud seeding in Arizona want a random sequence of days for their experiments. (Reference: Proceedings of the National Academy of Science, Vol. 68, pp. 649-652.) Suppose they have the following itinerary for consecutive days, where S indicates a day for cloud seeding and N indicates a day for no cloud seeding.

S

S

S

S

N

S

N

S

S

S

S

N

N

N

N

S

S

S

N

N

S

S

S

S

Test the sequence for randomness. Use α = 0.05.

Find the sample test statistic R, the number of runs.

Find the upper and lower critical values in Table 10 of Appendix II.

c1
c2

The following data represent annual percentage returns on Vanguard Total Bond Index for a sequence of recent years. This fund represents nearly all publicly traded U.S. bonds. (Reference: Morningstar Mutual Fund Analysis.)

0.5

9.5

-2.2

18.6

3.2

9.6

8.7

-0.7

11.7

8.6

8.4

7.2

Test the sequence for randomness about the median. Use α = 0.05.

Find the sample test statistic R, the number of runs.

Find the upper and lower critical values in Table 10 of Appendix II.

c1
c2

Answer 1