A student at a large high school selects a random sample of 145 students. For each, she records the grade level and their favorite color. She would like to know if there is convincing evidence that grade level is associated with favorite color. Let alpha is equal to 0 point 0 5 What are the hypotheses for this test?
Answer
A
cap h sub 0 : There is an association between grade level and color preference. cap h sub A : There is no association between grade level and color preference.
B
cap h sub 0 : Grade level is not independent of color preference. cap h sub A : Grade level is independent of color preference.
C
cap h sub 0 : Grade level is independent of color preference. cap h sub A : Grade level is not independent of color preference.
D
cap h sub 0 : The proportion of students’ favorite color is not the same in the grade levels. cap h sub A : The proportion of students’ favorite color is the same in the grade levels.
Explanation
For a test of association between two categorical variables, the null hypothesis states that the variables are independent, meaning there is no association. The alternative says they are not independent, meaning grade level and favorite color are associated. Therefore, choice C gives the correct hypotheses.
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