Question

These numbers have been drawn from a uniform distribution with range 1-40.

4, 6, 16, 12, 23, 19, 16 26, 14, 12, 12, 10, 3, 26, 35, 8, 30, 11, 14, 34, 37, 16, 36, 30, 18, 39, 24, 18, 39, 5, 12, 28, 4, 12, 34, 16, 35, 27, 15, 1

Test the sample for randomness using:

1. a Kolmogorov—Smirnov test.

Answer 1

The test has been done with help of R software.

Accoring to Kolmogorov Smirnov test, the p-value comes out to be 0.4097 and it indicates that there is sufficient evidence that there is a randomeness in the given data.

R code:

####### Test for Randomness #######################
x<-c(4, 6, 16, 12, 23, 19, 16, 26, 14, 12, 12, 10, 3,
26, 35, 8, 30, 11, 14, 34, 37, 16, 36, 30, 18, 39, 24,
18, 39, 5, 12, 28, 4, 12, 34, 16, 35, 27, 15, 1)
ks.test(x,"punif",1,40)
###### The End ####################################
Output:

> ####### Test for Randomness #######################
> x<-c(4, 6, 16, 12, 23, 19, 16, 26, 14, 12, 12, 10, 3,
+ 26, 35, 8, 30, 11, 14, 34, 37, 16, 36, 30, 18, 39, 24,
+ 18, 39, 5, 12, 28, 4, 12, 34, 16, 35, 27, 15, 1)
> ks.test(x,"punif",1,40)

One-sample Kolmogorov-Smirnov test

data: x
D = 0.14038, p-value = 0.4097
alternative hypothesis: two-sided

Warning message:
In ks.test(x, "punif", 1, 40) :
ties should not be present for the Kolmogorov-Smirnov test
> ###### The End ####################################
>