Sand and clay studies were conducted at the West Side Field Station of the University of California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of clay in the soil were recorded.

47.4 43.4 48.4 42.6 41.4 40.7 46.4 44.8 36.5 35.7 33.7 42.6

(i) Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B a value below the median.

(ii) Test the sequence for randomness about the median. 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.