Question

Suppose that nationwide, 20% of people in the U.S. attend religious services weekly, 25% attend religious services occasionally (less than weekly but more than just holidays), 15% attend on holidays only, and 40% do not attend religious services at all. In a random sample of people from one particular city, 12 attend services weekly, 14 attend occasionally, 3 attend on holidays only, and 8 do not attend at all. Conduct an appropriate test to determine whether religious service attendance in this city is consistent with the distribution observed nationwide. [To receive full credit, your response should be sure to state your hypotheses, find a test value, find a critical value or p-value, make your decision, and state your conclusion.]

Answer 1

Ho: religious service attendance in this city is consistent with the distribution observed nationwide

Ha: religious service attendance in this city is not consistent with the distribution observed nationwide

observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
12	0.200	7.40			2.859
14	0.250	9.25			2.439
3	0.150	5.55			1.172
8	0.400	14.80			3.124

chi square test statistic,X² = Σ(O-E)²/E =   9.595              
                  
level of significance, α=   0.05              
Degree of freedom=k-1=   4   -   1   =   3

Critical value =    7.8147   [ Excel function: =chisq.inv.rt(α,df) ]          
                  
P value =   0.0223   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value < α, Reject Ho                  
                  
so,  religious service attendance in this city is not consistent with the distribution observed nationwide

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