Question

Results from the National Health Interview Survey show that among the U.S. adult population, 45.9% do not meet physical activity guidelines, 3.5% meet only strength activity, 29.0% meet only aerobic activity, and 21.6% meet both strength and aerobic activity. We sampled 4475 adults from Ohio and the results were as follows: 50.0% do not meet physical activity guidelines, 5.0% meet only strength activity, 35.0% meet only aerobic activity, and 10.0% meet both strength and aerobic activity. Conduct an appropriate hypothesis test to determine if the distribution in physical activity among Ohioans is similar to the U.S. population. Interpret your results.

Answer 1

here we want to test the

null hypothesis H0: physical activity among Ohioans is similar to the U.S. population

alternate hypothesis H0: physical activity among Ohioans is not similar to the U.S. population

we use chi-square test and chi-squar=sum((O-E)²/E)=379.48 with k-1=4-1=3 df and

critical chi-square(0.05,3)=7.81 is less than calculated chi-squre=379.48, so we reject the null hypothesis and conclude that distribution in physical activity among Ohioans is not similar to the U.S. population.

following information has been generated

group	Expected% (US)	Observed%(Ohiaonas)	Expected frequency(E)	Observedfrequency(O)	(O-E)	(O-E)2/E
donot meet physical activity	45.9	50	2054.025	2237.5	183.475	16.39
strength	3.5	5	156.625	223.75	67.125	28.77
aerobic	29	35	1297.75	1566.25	268.5	55.55
both strength and aerobic	21.6	10	966.6	447.5	-519.1	278.78
sum=	100	100	4475	4475	0	379.48
					critical chi-square(0.05,3)=	7.81