Write down the steps for K-S test. The sequence of numbers 0.54, 0.75, 0.98, 0.12, and 0.68 has been generated. Use K-S test with ɑ=0.05 to learn whether the hypothesis that the numbers are uniformly distributed on the interval [0, 1] can be rejected. (Critical value Dɑ=0.565).

Step 1) H0: Ri~ Uniformly (0, 1)

H1: Ri~ is not Uniformly (0, 1)

Step 2) Number of random numbers= N= 5

Step 3) Arrange all random numbers in ascending order

0.12, 0.54, 0.68, 0.75, 0.98

Step 4)

$D^+ =Max (i/N-R_i)$

$D- = Max(R_i-((i-1)/N)$

$D_0 = Max (D^+, D-)$

$D+= 0.08$

$D-= 0.34$

$D_0=0.34$

Step 5) $D_{0.05}=0.565$

Step 6) $D_0\lt=D_{0.05}$

So we accepts $H_0$

It means that the given samples have property of uniformity.