Question

Consider the following two-digit random decimal numbers: 30, 61, 43, 04, 02, 75, 50, 99, 82, 41, 27, 85, 98, 59, 53, 11, 36, 74, 77, 30, 84, 72, 71, 30, 61, 98, 94, 54, 63, 99 Perform the run up and down test to check whether the series of two-digit numbers is random at 0.05 level of significance. (6) When comparing two simulation models, we sometimes use the same set of random numbers. Explain why? (a)

Answer 1

(a):

Using SPSS:

First Enter the data:

Value 10 11 12 13 14 15 16 17 18

19 | 20 | 21 22 233 24 25 26 27 28 29 30

Steps for Runs Test:

Analyze-->Non-parametric Test-->Runs

and then select the data:

Output:

Runs Test Value Test Value Cases < Test Value Cases >= Test Value Total Cases Number of Runs 16 .000 1.000 Asymp. Sig. (2-tailed) a. Median

Hypothesis:

H0 : Data is random

H1: Data is not random

p-value is 1 that is greater than 0.05, it's mean that is not significant and we fail to reject the null hypothesis,so our data is random.

(b):

When comparing two simulation models, we sometimes use the same set of random number because we want to achieve sharper comparisons and this is called correlated sampling or common random numbers.