Let Positive Daily S&P 500 Returns Define Up Days, and Negative

Essay

Let positive daily S&P 500 returns define up days, and negative daily S&P 500 returns define down days. A stockbroker wants to know if the up and down days of the S&P 500 occur randomly. For 30 trading days, there were 17 up days, 13 down days, four runs of up days, and four runs of down days.
A) Specify the competing hypotheses to determine whether the S&P 500 up and down days occur at random.
B) What is the value of the Wald-Wolfowitz runs test statistic?
C) At the 5% significance level, what is the decision and conclusion?