Question

1. (8 pts) 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

The null and alternate hypothesis are:

H0: Religious service attendance in this city is consistent with the distribution observed nationwide.

Ha: Religious service attendance in this city isn't consistent with the distribution observed nationwide.

	Weekly	Occasionaly	Holidays only	Do not attend	TOTAL
Observed (O)	12	14	3	8	37
Expected (E)	0.2(37)=7.4	0.25(37)=9.25	0.15(37)=5.55	0.40(37)=14.8	37
	2.86	2.44	1.17	3.12	9.59

Test statistic value =

The p-value is given by:

Let the level of significance be 5%.

Since p-value is less than 0.05, so we have sufficient evidence to reject the null hypothesis H0.

Thus we can conclude that religious service attendance in this city isn't consistent with the distribution observed nationwide.