Question

For the following sequence of sample nominal data (with two categories), conduct a runs test for randomness, using α = 0.05.

Y N Y N N Y N Y Y Y N Y N Y N Y Y Y N Y N Y N N Y Y Y Y N Y N Y N Y Y

Identify the value of the TEST STATISTIC used in this runs test.

Answer 1

GIVEN:

The following sequence of sample nominal data with two categories:

Y N Y N N Y N Y Y Y N Y N Y N Y Y Y N Y N Y N N Y Y Y Y N Y N Y N Y Y

Number of Y's

Number of N's

Y N Y N N Y  N Y Y Y N Y  N Y N Y Y Y N Y N Y N N Y Y Y Y N Y N Y N Y Y

Number of runs

(A run is a sequence within a series in which one of the 2 alternatives occurs on consecutive trials.)

HYPOTHESIS:

The hypothesis is given by,

The sequence is random.

The sequence is not random.

LEVEL OF SIGNIFICANCE:

TEST STATISTIC:

which follows standard normal distribution

where

and

CALCULATION:

Let  

Let  

Now

CRITICAL VALUE:

The z critical value at significance level is .

CONCLUSION:

Since the calculated z test statistic (2.58) is greater than the z critical value (1.96), we fail to reject null hypothesis and conclude that the sequence is random.