Question

A researcher would like to determine if the proportion of households without health insurance coverage differs with household income. Suppose the following data were collected from 700 randomly selected households. (hint: chapter 12) ter 12) Household Income Less than 25000 25000_to_ 49999 50000_to_74999 75000 or more Yes No 5 4 20 1 41 42 203 36 172 3 2 1 Using a=0.01, perform a chi-square test to determine if the proportion of households without health insurance differs by income bracket. 6) Determine the correct null and alternative hypotheses 7) What is the test statistic and what is the critical value? (show your work). 8) State and interpret your conclusion(show your work).

Answer 1

6)

Null hypothesis:Ho: proportion of household without health insurance are equal across income ranges.

Alternate hypothesis: Ha: proportion of household without health insurance differs across income ranges.

7)

degree of freedom(df) =(rows-1)*(columns-1)=		3
for 3 df and 0.01 level , critical value       χ2=		11.345
Decision rule : reject Ho if value of test statistic X2>11.345

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Yes	No	Total
	<25000	60.257	13.743	74.00
	25000-49999	149.014	33.986	183.00
	50000-74999	194.614	44.386	239.00
	75000 or more	166.114	37.886	204.00
	total	570.00	130.00	700.00
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	<25000	0.650	2.849	3.4986
	25000-49999	0.431	1.8899	2.3209
	50000-74999	0.361	1.5843	1.9456
	75000 or more	0.209	0.9144	1.1229
	total	1.6506	7.2374	8.888
test statistic X2 =		8.888

8)

since test statistic < critical value.

we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that proportion of household without health insurance differs across income ranges.