written 2.6 years ago by | modified 19 months ago by |
{0.594, 0.928, 0.515, 0.055, 0.507, 0.351, 0.262, 0.797, 0.788, 0.442, 0.097, 0.798, 0.227, 0.127, 0.474, 0.825, 0.007, 0.182, 0.929, 0.852} Use $\alpha$=0.05, $\chi ^2 _{(0.05,1)}$= 3.84 p
written 2.6 years ago by | modified 19 months ago by |
{0.594, 0.928, 0.515, 0.055, 0.507, 0.351, 0.262, 0.797, 0.788, 0.442, 0.097, 0.798, 0.227, 0.127, 0.474, 0.825, 0.007, 0.182, 0.929, 0.852} Use $\alpha$=0.05, $\chi ^2 _{(0.05,1)}$= 3.84 p
written 2.6 years ago by | • modified 2.6 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.