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. Complete parts a through c.

Household_Income   Yes   No
Less_than_25,000 53 20
25,000_to_49,999 143 41
50,000_to_74,999 205 37
75,000_or_more 174 27

a. Using alpha= ​0.01, perform a​ chi-square test to determine if the proportion of households without health insurance differs by income bracket.

What is the test statistic?

What is the critical value?

State the conclusion

What is the p-value?

What does this p-value means?

How does income appear to impact the likelihood that a household has insurance coverage?

Answer 1

applying chi square test:

Expected	Ei=row total*column total/grand total	Yes	No	Total
	<25000	59.96	13.04	73
	25000-49999	151.14	32.86	184
	50000-74999	198.79	43.21	242
	>75000	165.11	35.89	201
	total	575	125	700
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	<25000	0.8088	3.7206	4.529
	25000-49999	0.4387	2.0180	2.457
	50000-74999	0.1943	0.8936	1.088
	>75000	0.4790	2.2033	2.682
	total	1.921	8.836	10.756

a)

test statistic =10.756

b)

for 3 df and 0.01 level of signifcance critical value      χ2=

11.345

c)

conclusion :fail to reject HO as test statistic is less than crtiical value

we can not conclude that income appear to impact the likelihood that a household has insurance coverage

d)

p value =0.0131

it means that there is a 0.0131 probability of getting a test statistic as extreme or more ;if there is no impact of likelihood that a household has insurance coverage