Astronomy: Earth’s Rotation Changes in the earth’s rotation are exceedingly small. However, a very longterm trend could be important. (Reference: Journal of Astronomy, Vol. 57, pp. 125–146). 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 5 0.05.

please provide the following information.

(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.AppendixLO1