Question

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 α = 0.05. what are the hypotheses for this test?
○ h₀: there is no association between grade level and whether the student makes their bed in the morning.
hₐ: there is an association between grade level and whether the student makes their bed in the morning.
○ h₀: there is an association between grade level and whether the student makes their bed in the morning.
hₐ: there is no association between grade level and whether the student makes their bed in the morning.
○ h₀: there is a difference in the distribution of grade level and whether the student makes their bed in the morning.
hₐ: there is no difference in the distribution of grade level and whether the student makes their bed in the
morning.
● h₀: there is no difference in the distribution of grade level and whether the student makes their bed in the
morning.
hₐ: there is a difference in the distribution of grade level and whether the student makes their bed in the morning.

Explanation:

In hypothesis testing for association (or independence in a two - way table context), the null hypothesis \(H_0\) always assumes no association (or no difference in distributions if we consider the relationship between two categorical variables). The alternative hypothesis \(H_a\) is the claim we are trying to find evidence for, which is that there is an association (or a difference in distributions).

For the relationship between grade level (a categorical variable with levels: ninth, tenth, eleventh, twelfth) and whether a student makes their bed (a categorical variable with two levels: yes/no), the null hypothesis is that there is no association (or no difference in the distribution of bed - making behavior across grade levels), and the alternative hypothesis is that there is an association (or a difference in the distribution of bed - making behavior across grade levels).

Answer:

The first option: \(H_0\): There is no association between grade level and whether the student makes their bed in the morning. \(H_a\): There is an association between grade level and whether the student makes their bed in the morning.