Question

Lucas wants to determine if there is a relationship between a person's Height and income. He takes a random sample of participants and records their Heights and incomes. He plans to conduct a Chi- squared test to analyze his results, treating income as a categorical variable by binning it into ranges (e.g. Under $38000, $38000 - $81000, etc.), and treating height as a categorical variable by considering it in ranges (e.g. 60-64 inches, 64-68 inches, etc.). What hypotheses would he use for his test? Ho: For each income category, the proportion of subjects that fall into each Height category will be the same. Ha: For each income category, the proportion of subjects that fall into each Height category will not be the same. Ho: The proportion of subjects that fall into each Height category will be the same. Ha: The proportion of subjects that fall into each Height will not be the same. Ho: Income is independent from Height. Ha: Income and Height are dependent. Ho: The proportion of subjects that fall into each income category will be the same. Ha: The proportion of subjects who fall into each income category will not be the same.

Answer 1

Answer:

H₀: Income is independent from height.

H_a: Income and Height are dependent.

Explanation:

The required null and alternative hypotheses for the Chi-square test for the independence between two categorical variables are given as below:

Null hypothesis: H₀: Two categorical variables income and height are independent.

Alternative hypothesis: H_a: Two categorical variables income and height are dependent.

We can also write these hypotheses as below:

Null hypothesis: H₀: Income is independent from height.

Alternative hypothesis: H_a: Income and Height are dependent.