Question

Exercise 6. Test the claim that the following sequence of numbers is not random at α = 0.025 using the rank test for randomness.

250

221

205

225

215

216

216

236

246

200

207

245

201

229

248

Answer 1

Here we will use RUNS test to check if the sequence of numbers are random or not\

So, Hypotheses are:

Ho: Sequence of Numbers are random

Ha: Sequence of Numbers are not random

Now, Arranging the above data in increasing order,

200
201
205
207
215
216
216
221
225
229
236
245
246
248
250

Hence Median = 8th term = 221

Labeling each Number with either a U if the Number is greater than the median (221), or an L if the Number is less than or equal to median (221), we get:

250	U
221	L
205	L
225	U
215	L
216	L
216	L
236	U
246	U
200	L
207	L
245	U
201	L
229	U
248	U

So, number of Runs, N = 9

No of U, n1 = 7

No of L, n2 = 8

From Runs Test table, we get

Lower Limit = 4

Upper Limit = 13

Since N lies between Lower and Upper Limit. So, we cannot reject the Null Hypotheses.

Or by p-value we get, P = 0.387 which is more than 0.025.

So, we cannot reject the Null Hypotheses.

Hence we can say that Sequence of Numbers are Random