Question

Find the χ2 (chi-square) value and P-value from these results. Cite my P-value for your answer.

252	24
208	23

my P-value = ________

(1) My P-value is about 0.238

(2) My P-value is about 0.762

(3) My P-value is about 0.374

(4) My P-value is about 0.626

Answer 1

Given :

Contegency table :

			Total
	252	24	276
	208	23	231
Total	460	47	507

Expected frequency = (row sum * column sum)/Grand sum

E1 = 276*460/507 = 250.14

E2 = 276*47/507 = 25.586

E3 = 231*460/507 = 209.586

E4 = 231*47/507 = 21.414

Chi square goodness of fit test :

Category	Observed frequency (Oi)	Expected frequency (Ei)	(Oi-Ei)^2/Ei
1	252	250.414	0.01
2	24	25.586	0.0983
3	208	209.586	0.012
4	23	21.414	0.1175
Total	507	507	0.238

Test statistic :

$\chi^2$ = $\sum$ (Oi-Ei)^2/Ei = 0.238

Degree of freedom = (r-1)(c-1) = (2-1)(2-1) = 1*1 = 1

P-value : P-value corresponding to $\chi^2$ = 0.238 and df = 1 is 0.626

Therefore the χ2 (chi-square) value = 0.238 and P-value = 0.626

Answer - option 4