Exhibit 20.12.A magician has a coin that may or not be fair.The results of 30 flips of the coin are: H H T H T H H T H H T H H T H T H H H T T T T T H H H H H T. Refer to Exhibit 20.12.To determine if the coin is fair using the Wald-Wolfowitz runs test,the competing hypotheses are:

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The Wald-Wolfowitz runs test is used to test whether the sequence of data is random or not. The null hypothesis is that the data is random, and the alternative hypothesis is that the data is not random. In this case, the sequence of heads and tails is tested to see if the coin is fair or not. The number of runs in the sequence is calculated, and this is compared to the expected number of runs for a fair coin. The expected number of runs is calculated as (2n1n2)/(n1+n2)+1, where n1 and n2 are the number of heads and tails in the sequence, and n1+n2 is the total number of flips. The value of Z is calculated as (R-E(R))/standard deviation of R. If the absolute value of Z is greater than the critical value of the test statistic, then the null hypothesis is rejected at the given level of significance. Choice (B) is correct because it accurately states the competing hypotheses for the Wald-Wolfowitz runs test, which are whether the coin is fair or not.