Question

The following sequence of 28 consecutive data values was collected. This sequence was found to contain ten 0's and eighteen 1's. Conduct a runs test for randomness for this sequence at the 0.05 significance level, and test the claim that the order of this sequence is random.

0111011110001101100101111101

Round your answers to 3 places after the decimal point, if necessary.

(a) Find the value of the test statistic.

     Test statistic's value:

(b) Find the critical values. List both critical values in the answer box with a comma between them.

     Critical values:

(c) What is the correct conclusion of this test?

• There is not sufficient evidence to warrant rejection of the claim that the order of this sequence is random.
• There is sufficient evidence to warrant rejection of the claim that the order of this sequence is random.
• There is not sufficient evidence to support the claim that the order of this sequence is random.
• There is sufficient evidence to support the claim that the order of this sequence is ran

Answer 1

a) The test statistic is given by:

, where R is the number of runs, is the expected number of runs and S_R is the standard deviation of the number of runs. and S_R is given as:

. Here n₁ and n₂ denote the number of positive and negative values in the series. Thus =13.857 and S_R = 2.376. Now the number of runs here is 14. Thus the test statistic is  0.06

b) The critical values at a level of significance of 0.05 are (-1.96, 1.96)

c) The conclusion of the test is:

There is not sufficient evidence to warrant rejection of the claim that the order of this sequence is random.