| A researcher would like to determine if theproportion of households without health insurance coverage differswith household income. Suppose the following data were collectedfrom 700700 randomly selected households. Complete parts a through c. | Heath Insurance   |
Household Income | Yes | No |
|---|
Less than​ $25,000 | 55 | 22 |
​$25,000 to​ $49,999 | 145 | 40 |
​$50,000 to​ $74,999 | 201 | 40 |
​$75,000 or more | 177 | 20 |
a. Using alphaαequals=​0.01, perform a​ chi-square test todetermine if the proportion of households without health insurancediffers by income bracket.
Choose the correct null and alternative hypotheses below.
A.
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
B.
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
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​:
Not all​ p's are equal
What is the test​ statistic?
chi squaredχ2equals=nothing
​(Round to two decimal places as​ needed.)
What is the critical​ value?
chi Subscript 0.01 Superscript 2χ20.01equals=nothing
​(Round to two decimal places as​ needed.)
State the conclusion.
â–¼
Do not reject
Reject
Upper H 0H0.
There is
â–¼
sufficient
insufficient
evidence that the proportion of households without healthinsurance differs by income bracket.
b. Interpret the meaning of the​ p-value.
What is the​ p-value?
​p-valueequals=nothing
​(Round to three decimal places as​ needed.)
What does the​ p-value mean? Select the correct choice and fillin the answer box to complete your choice.
​(Round to one decimal place as​ needed.)
A.There is a
nothing​%
chance of observing a test statistic value greater than theactual test statistic value if there is no difference in theproportion of households without health insurance.
B.There is a
nothing​%
chance of rejecting the null hypothesis when it should not berejected.
C.Given a very large number of​ samples, there is a
nothing​%
chance of observing a sample with the given data.
c. How does income appear to impact the likelihood that ahousehold has insurance​ coverage?
A.
The proportion of households without health insurance is alwaysuniform 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 increasesas income increases.
D.The proportion of households without health insurance
differs by income bracket.
Click to select your answer(s).
