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 chisquare 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 pvalue.
What is the pvalue?
pvalue equals=
(Round to three decimal places as needed.)
What does the pvalue 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.
applying chi square test:
Expected  E_{i}=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 χ^{2}  =(O_{i}E_{i})^{2}/E_{i}  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 X^{2} =10.61
critical value χ2 _{0.01equals} =11.34
pvalue =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.
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