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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 52 23
$25,000 to $49,999 143 40
$50,000 to $74,999 200 35
$75,000 or more 177 30

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

i. State the null hypothesis

ii. What is the test statistic?

iii. What is the critical value?

iv. State the conclusion.