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.

(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.

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