**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

H_{0}: Arrangement is random

H_{1}: 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, n_{1} = 7

Number of T, n_{2} =8

Test Statistic = 7 (number of runs)

**Step 3: **Lookup Critical values in table of runs tests

At = 0.05 significance, n_{1} = 7, n_{2} =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