Hypothesis Testing Question 19 – Run Test ( Trees were planted…)

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  {displaystyle varepsilon !}varepsilon !  = 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, n1 = 13
Number of D, n2 = 9

 

Step 3: Lookup Critical values in table of runs tests
At  varepsilon !  = 0.05 signnificance, n1 = 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