Is there an association between grade level and whether the student makes their bed in the morning? To investigate, the principal at a large high school selects a random sample of 84 students and classifies them as being in ninth, tenth, eleventh, or twelfth grade, and whether they make their bed. He would like to determine if there is convincing evidence of an association. 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 whether the student makes their bed in the morning. cap h sub A : There is no association between grade level and whether the student makes their bed in the morning.
B
cap h sub 0 : There is no difference in the distribution of grade level and whether the student makes their bed in the morning. cap h sub A : There is a difference in the distribution of grade level and whether the student makes their bed in the morning.
C
cap h sub 0 : There is no association between grade level and whether the student makes their bed in the morning. cap h sub A : There is an association between grade level and whether the student makes their bed in the morning.
D
cap h sub 0 : There is a difference in the distribution of grade level and whether the student makes their bed in the morning. cap h sub A : There is no difference in the distribution of grade level and whether the student makes their bed in the morning.
Explanation
This is a test of association between two categorical variables: grade level and whether a student makes their bed. The null hypothesis states that the variables are not associated; the alternative states that they are associated. Therefore, choice C gives the correct hypotheses. The significance level of 0.05 affects the decision rule, not the hypotheses.
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