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 700700 randomly selected households. Complete parts a through c.	Heath Insurance
	Household Income	Yes	No
	Less than​ $25,000	55	21
	​$25,000 to​ $49,999	140	45
	​$50,000 to​ $74,999	200	38
	​$75,000 or more	171	30

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

Choose the correct null and alternative hypotheses below.

A.

Upper H 0H0​:

p 1 equals p 2 equals p 3 equals p 4p1=p2=p3=p4

Upper H 1H1​:

Not all​ p's are equalYour answer is correct.

B.

Upper H 0H0​:

Not all​ p's are equal

Upper H 1H1​:

p 1 equals p 2 equals p 3 equals p 4p1=p2=p3=p4

C.

Upper H 0H0​:

p 1 not equals p 2 not equals p 3 not equals p 4p1≠p2≠p3≠p4

Upper H 1H1​:

p 1 equals p 2 equals p 3 equals p 4p1=p2=p3=p4

D.

Upper H 0H0​:

p 1 equals p 2 equals p 3 equals p 4p1=p2=p3=p4

Upper H 1H1​:

p 1 not equals p 2 not equals p 3 not equals p 4p1≠p2≠p3≠p4

What is the test​ statistic?

χ2=_______

​(Round to two decimal places as​ needed.)

What is the critical​ value?

χ2 0.01equals=__________

​(Round to two decimal places as​ needed.)

State the conclusion.

________ Upper H 0H0. There is _________ evidence that the proportion of households without health insurance differs by income bracket.

b. Interpret the meaning of the​ p-value.

What is the​ p-value?

​p-value equals=

​(Round to three decimal places as​ needed.)

What does the​ p-value mean? Select the correct choice and fill in the answer box to complete your choice.

​(Round to one decimal place as​ needed.)

A.There is a ___​% chance of rejecting the null hypothesis when it should not be rejected.Your answer is not correct.

B.Given a very large number of​ samples, there is a ___ % chance of observing a sample with the given data.

C.There is a _____ % chance of observing a test statistic value greater than the actual test statistic value if there is no difference in the proportion of households without health insurance.

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

A.The proportion of households without health insurance is always uniform and does not depend on income bracket.

B.The proportion of households without health insurance does not differdoes not differ by income bracket.

C.The proportion of households without health insurance differs by income bracket.Your answer is correct.

D.The proportion of households without health insurance increases as income increases.

Answer 1

applying chi square test:

Expected	Ei=row total*column total/grand total	Yes	No	Total
	first class	61.45	14.55	76
	Business class	149.59	35.41	185
	Economy class	192.44	45.56	238
	Economy class	162.52	38.48	201
	total	566	134	700
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	first class	0.6773	2.8608	3.538
	Business class	0.6143	2.5946	3.209
	Economy class	0.2970	1.2545	1.551
	Economy class	0.4422	1.8677	2.310
	total	2.031	8.578	10.608

test statistic X² =10.61

critical​ value χ2 _0.01equals =11.34

​p-value =0.014

C.There is a __1.4___ % chance of observing a test statistic value greater than the actual test statistic value if there is no difference in the proportion of households without health insurance.