Dr. Gill wants to arrange the answers to a true–false exam in random order. The answers in order of occurrence follow.

T‑T‑T‑T‑F‑T‑T‑F‑F‑T‑T‑T‑T‑F‑F‑F‑F‑F‑F‑T‑T‑T‑T‑T‑T

Test the sequence for randomness using a = 0.05.

(a) State the test used.

(b) Give a. State the null and alternate hypotheses.

(c) Find the sample test statistic.

(d) For the sign test, rank-sum test, and Spearman correlation coef­ficient test, fi­nd the P-value of the sample test statistic. For the runs test of randomness, ­find the critical values from Table 10 of Appendix II.

(e) Conclude the test and interpret the results in the context of the application