Question

I flip a coin 20 times and record the results as follows: T T H H H T H H T T H H H T T T T T T H. Use the runs test for randomness at a significance level of 0.05 to test this sequence of coin flips for randomness.

Answer 1

Solution:

Givem: A coin is flipped 20 times

T T H H H T H H T T H H H T T T T T T H

We have to use  the runs test for randomness at a significance level of 0.05 to test this sequence of coin flips for randomness.

Step 1) State H0 and H1:

H0: The sequence of coin flips is random

Vs

H1: The sequence of coin flips is not random

Step 2) Find r = number of runs.

Run is an unbroken sequence of simmilar symbols

thus we have:

T

T

H

H

H

T

H

H

T

T

H

H

H

T

T

T

T

T

T

H

1

2

3

4

5

6

7

8

Thus

Number of runs are:

r = 8

m = Number of symbols of type T = 11

n = Number of symbols of type H = 9

Step 3) Find critical value using run test critical value table.

thus critical values are:

a = 6 , b = 16

Step 4) Decision rule:

If a < r < b, then we do not reject the null hypothesis H0, otherwise we reject H0.

Since a = 6 < r = 8 < b = 16, we do not reject the null hypothesis H0.

Step 5) Conclusion:

At 0.05 level of significance , we conclude that the sequence of coin flips is random