Test the following random numbers for independence by Poker test.

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written 5.6 years ago by

teamques10 ★ 68k

• modified 5.6 years ago

Poker Test

N = 20

Let us assume 3 digit nos. { 594, 928, 515, ..., 852}

Step 1: Define hypothesis

$H_0: R_i \sim$ independently

$H_a: R_i \not{\sim}$ independently

Step 2: Generate frequency distribution table

Combination i	Observed freq $O_i$	Exp. Freq. $E_i = P \times N$	$\frac{\left(b_{1}-E_{1}\right)^{2}}{E_{i}}$
3 diff digits, 1	10	$0.72 \times 20 = 14.4$	1.34
3 diff digits, 2	0	$0.01 \times 20 = 0.2$	3.45
Exactly 1 pair, 3	10	$0.27 \times 20 = 5.4$	3.45

Step 3: Compute the sample test statistics

$\begin{aligned} \chi_{0}^{2} &= \sum_{i=1}^{n} \frac{\left(0_{i}-E_{i}\right)^{2}}{E_{i}}\\ &= 1.34 + 3.45 \\ &= 4.79 \end{aligned}$

Step 4: Determine critical value for the specified significance level $\alpha$ with (n-1) diff

$\because \quad \alpha=0.05 \quad n-1 = 2 - 1 = 1$

$\chi_{0.05,1}^2 = 3.84 \ (given)$

Step 5:

$\chi_0^2 = 4.79 \gt chi_{0.05, 1} = 3.84$

$\therefore$ Reject $H_0$

i.e. Random nos are not independent.

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