Can you please explain to me how the value is .004?? This is a completed answer but I am unsure how the pvalue is .004.

1. Use the percentages to the distribution of rural and urban communities

	Catholic	Percentages	Protestant	Percentages	Other	Percentages
Favor legalization	8	26.67	24	48	15	75
Oppose legalization	22	73.33	26	52	5	25
Total	30	100.00%	50	100.00%	20	100

b. the first step is to state the null hypothesis and an alternate-hypotheses.

H₀ church and legalization are independent

H₁church and legalization are not independent

Chi-square test for independence test

Give the data is as below

Matrix	column 1	column 2	olumn 3
row1	8	24	15
row2	22	26	5
Total	30	50	20

Calculations for E table matrix

E-table	Column 1	Column 2	Column 3
row1	row1 * col 1 / N	row1 * col 2 / N	row1 * col 3/ N
row2	row2 * col 1 / N	row2 * col 2 / N	row2 * col 3 / N

Expected frequencies calculated by applying for E-table matrix formula

E-table	Column 1	Column 2	Column 3
Row1	14.1	23.5	9.4
Row2	15.9	26.5	10.6

Calculate chi-square test statistic using given observed frequencies.

Calculated expected frequencies from above

Oi	Ei	Oi - Ei	(Oi - Ei)2	(Oi - Ei)2 /Ei
8	14.1	-6.1	37.21	2.639
24	23.5	0.5	0.25	0.010
15	9.4	5.6	31.36	3.336
22	15.9	6.1	37.21	2.340
26	26.5	-0.5	0.25	0.009
5	10.6	-5.6	31.36	2.958

Y²o = 11.293

Set up null vs alternative as:

Null, H_o: no relation between x and y or x and y are independent

Alternative: H₁: exists a relation between x and y or x and y are dependent

Level of significance, alpha = 0.05

From the standard normal table, the chi-square value at right-tailed y²alpha/2 = 5.991

Since our test is right-tailed, reject H_o when y²> 5.991

We use test statistic y² o =(Oi - Ei)^{2 /}Ei

From the table, y²o = 11.293

Critical value

The value of y² alpha at level of significance 0.05 with d.f (r - 1)(c - 1) = (2 -1) * (3-1)

= 2

We got [y²o] > y² alpha and here we reject the null hypothesis

Y²p-value = (.003875) rounded to 0.004

Answer in summary:

Null, H_o: no relation between x and y or x and y are independent

Alternative: H₁: exists a relation between x and y or x and y are dependent

Test statistic: 11.293

Critical value: 5.991

p-value: 0.004

decision: reject null hypothesis