Dr. Gill wants to arrange the answers to a true-false exam in random order. The answers in order of occurrence are shown below. T T T T F T T F F F F T T F F F F F F T T T T T T Test the sequence for randomness using ? = 0.05. (c) Find the sample test statistic. (d) For the sign test, rank-sum test, and Spearman correlation coefficient test, find the P-value of the sample test statistic. For the runs test of randomness, find the critical values from Table 10 of Appendix II. c1 c2
Dr. Gill wants to arrange the answers to a true-false exam in random order. The answers in order of occurrence are shown below.
| T | T | T | T | F | T | T | F | F | F | F | T | T | F | F | F | F | F | F | T | T | T | T | T | T |
Test the sequence for randomness using ? = 0.05.
(c) Find the sample test statistic.
(d) For the sign test, rank-sum test, and Spearman
| c1 | |
| c2 |
Given : Dr. Gill wants to arrange the answers to a true-false exam in random order. The answers in order of occurrence provided .
The number of runs for this order is 7.
There are 14 True and 11 false in the sequence.
n1 = 14 , n2 = 11
Definition : We will code values above the median as positive and values below the median as negative.
A run is defined as a series of consecutive positive (or negative) values. The runs test is defined as:
H0: the sequence was produced in a random manner
Ha: the sequence was not produced in a random manner
Test Statistic: The test statistic is
where ,
=
=
with n1 and n2 denoting the number of positive and negative values in the series.
Sample test statistic : = 0.09063
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