Chi-Square Test of Association/Independence — Quiz
Question 9 • Statistics
A teacher selects a random sample of 56 students from her large high school. For each student, she records the length of their hair and whether they play a sport. She would like to know if there is convincing evidence that hair length is associated with playing a sport. Let alpha is equal to 0 point 0 5 What are the hypotheses for this test?
Answer
A
cap h sub 0 : Hair length is independent of playing a sport. cap h sub A : Hair length is not independent of playing a sport.
B
cap h sub 0 : Hair length is not independent of playing a sport. cap h sub A : Hair length is independent of playing a sport.
C
cap h sub 0 : The proportion of students with differing hair lengths is not the same if they play sports. cap h sub A : The proportion of students with differing hair lengths is the same if they play sports.
D
cap h sub 0 : There is an association between hair length and playing a sport. cap h sub A : There is no association between hair length and playing a sport.
Explanation
This is a test of whether two categorical variables—hair length and playing a sport—are associated. The null hypothesis states that the variables are independent; the alternative states that they are not independent, meaning there is an association. Therefore, the correct choice is A: hair length is independent of playing a sport under the null, and not independent under the alternative.
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