**Question 19**

Trees planted along the road were checked for which ones are healthy(H) or deseased (D) and the following arrangement of the trees were obtained:

H H H H D D D H H H H H H H D D H H D D D

Test at the

= 0.05 signnificance wether this arrangeemnt may be regarded as random

**Solution Steps**

**Stetp 1:** State the null and alternate hypothesis

H0: Arrangement is random

H1: Arrangement is not random

**Step 2**: Calculate the number of runs, H and D

H H H H D D D H H H H H H H D D H H D D D D

Number of runs is given by R = 6

Number of H, n_{1} = 13

Number of D, n_{2} = 9

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

At = 0.05 signnificance, n_{1 = 13, n2 = 9}

**Step 4: **State your Conclusion

In this case , since the absolute value calculated is less than the critical value, we reject the null hypothesis and conclude that the arrangement is not random

**Note about the Run Test**

The Run Test (which is also the Wald-Wolfowitz runs test) is a non-parametric statistical test that tests the randomness of a hypothesis for a 2-valued sequence of data.

It is used to test the hypothesis that the elements of the sequence are mutually independent