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 S&P 500 up and down days occur at random.
B)What is the value of the Wald-Wolfowitz runs test statistic R?
C)At the 5% significance level,what is the decision and conclusion?