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.

H TTT HH TTTT HH T 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 $varepsilon !$ = 0.05 significance, n₁ = 7, n₂ =8
Upper critical value = 4
Lower critical value = 13

Step 4: Make Your Decision
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