Question

# A researcher would like to determine if the proportion of households without health insurance coverage differs...

 Household Income Yes No 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 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.

#### Homework Answers

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.

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