Changes in the earth’s rotation are exceedingly small. However, a very long-term trend could be important. Let I represent an increase and D a decrease in the rate of the earth’s rotation. The following sequence represents historical increases and decreases measured every consecutive ­fifth year.

D D D D D I I I D D D D D I I I I I I I I I I D I I I I I

Test the sequence for randomness. Use a = 0.05.

(a) What is the level of signifi­cance? State the null and alternate hypotheses.

(b) Find the sample test statistic R, the number of runs.

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

(d) Conclude the test.

(e) Interpret the conclusion in the context of the application.