Question

Consider the following study results concerning Age and Church Attendance:

                                                                                                Age

Church Attendance         20-29                     30-39                     40-49                     50-59

Yes 21                           63                           94                           72

No 69                           87                           106                         78

Test to see if the proportion of people who attend church is the same for all age groups (95% confidence).

What is the value of the test statistic?

What is the p-value?

What is your decision concerning the null hypothesis and your conclusion?

Answer 1

Null hypothesis:Ho: proportion of people who attend church is the same for all age groups

Alternate hypothesis:Ho: proportion of people who attend church is not the same for all age groups

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	20-29	30-39	40-49	50-59	Total
	yes	38.1356	63.5593	84.7458	63.5593	250
	No	51.8644	86.4407	115.2542	86.4407	340
	total	90	150	200	150	590
chi square    χ2	=(Oi-Ei)2/Ei	20-29	30-39	40-49	50-59	Total
	yes	7.700	0.005	1.011	1.121	9.8360
	No	5.661	0.0036	0.7431	0.8242	7.2324
	total	13.3611	0.0085	1.7536	1.9451	17.068
test statistic X2 =	17.068

degree of freedom(df) =(rows-1)*(columns-1)=

3

p value from excel: chidist(17.068,3-1) =0.0007

since p value <0.05 ; we reject null hypothesis

we have sufficient evidence at 0.05 level to conclude that  proportion of people who attend church is not the same for all age groups