There is no relationship between household income level and home-ownership-v.-renting. Household income level varies much more than home-ownership-v.-renting proportions. Household income level and home-ownership-v.-renting are independent. There is a relationship between household income level and home-ownership-v.-renting. b) The χ2χ2test statistic value is:

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Researchers are investigating household-income level and whether the family owns their home or rents, in a particular city. They will consider the proportion of high-income households who own their home and the proportion of low-income households who own. They want to check whether the two categorical variables (income level and home-own-v.-rent) are related. Test at the 0.1 significance level.

Table of number of households in each sub-category.

Data Own Rent
high-income 58 37
low-income 31 50



a) Identify the correct alternative hypothesis for this test.

  • There is no relationship between household income level and home-ownership-v.-renting.
  • Household income level varies much more than home-ownership-v.-renting proportions.
  • Household income level and home-ownership-v.-renting are independent.
  • There is a relationship between household income level and home-ownership-v.-renting.



b) The χ2χ2test statistic value is:   

c) The P-value is: 

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