# Hypothesis Testing Question 20 – Run Test( Suppose we flip a coin…)

Question 20
Suppose we flip a coin n = 15 times and come up with the following arrangements

H T T T H H T T T T H H T H H

(H = head, T = tail)

Test at the alpha = 0.05 significance level whether this arrangement may be regarded as random.

Solution Steps
Step 1: State the null and alternate hypothesis
H0: Arrangement is random
H1: Arrangement is not random

Step 2: Calculate the Test Statistic (Number of Runs)
Normally you separate each of the runs so that you would be able to count them.

TTT  HH  TTTT  HH  HH

Number of runs is given by r = 7
Number of H, n1 = 7
Number of T, n2 =8

Test Statistic = 7 (number of runs)

Step 3: Lookup Critical values in table of runs tests
At    = 0.05 significance, n1 = 7, n2 =8
Upper critical value =  4
Lower critical value = 13

Since r = 10 which is between 4 and 13, we accept the null hypothesis (we fail to reject it)

Step 5: Draw a Conclusion
There are not enough evidence to reject the claim hat the pattern of occurrence of heads and tails is determined by a random process