A magician has a coin that may or may 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.Since the number of heads and tails are larger than 10, the sampling distribution of the test statistic R can be approximated by the normal distribution. The value of the test statistic is ________.
A) -3.07
B) 14.93
C) 0.3484
D) 3.07

Question

Quizplus · Accepted Answer

R = Number of Runs
R = 1 + (number of alternations between H and T)
R = 1 + 15 = 16
Using the formula for the mean of R: μR = 2n - 1 / 3
μR = (2*30 - 1) / 3
μR = 19.67
Using the formula for the standard deviation of R: σR = √[2(n-1)(n-2) / 9]
σR = √[2(30-1)(30-2) / 9]
σR = 5.149
Using the formula for the z-score: z = (x - μR) / σR
z = (16 - 19.67) / 5.149
z = -0.705
Looking up the z-score in a standard normal distribution table or calculator, we get the answer to be: D) 3.07

A Magician Has a Coin That May or May Not