Answer to Question #152675 in Statistics and Probability for Sharaf

Question

Following is a sequence of heads (H) and tails (T) 

in tossing a coin 14 times. 

 HTTHHHTHTTHHTH 

 Test whether the heads and tails occur in random 

order.

Answer 1

For the given sequence,

the sample size, n = 14,

number of heads, n1= 8

number of tails, n2= 6

Then for n1 = 8 and n2 = 6 and alpha = 0.05:

R_L= 4, R_U = 11

number of runs of H, R1 =5

number of runs of T, R2= 4

so that R=R1 + R2 = 5 + 4=9

Since the observed value of $R = 9 \in [4,11]$, we accept H0. It means that the heads and tails occur in random order or it can be said that the coin is unbiased.