Question

30 multiple choice 1 point
state the null hypothesis.

is achieving a basic skill level in a subject independent to the location of the school? a random sample of students categorized by the location of school and the number achieving basic skills in three subjects is shown in the table.

two - way table location vs subject

location of school	reading	math	science
suburban	63	66	65

state the null hypothesis for a chi - square test for independence.

• skill level in a subject is greater than location.
• skill level in a subject is not independent of location.
• skill level in a subject is related to location.
• cannot be determined.
• skill level in a subject is independent of location.

Explanation:

For a Chi - Square test for independence, the null hypothesis ($H_0$) states that the two categorical variables are independent of each other. In this problem, the two variables are the skill level in a subject (categorized by the number of students achieving basic skills in different subjects) and the location of the school (urban or suburban). So the null hypothesis should be that the skill level in a subject is independent of the location of the school. Let's analyze the options:

• "Skill level in a subject is greater than location" is incorrect as we are not comparing magnitudes in this context.
• "Skill level in a subject is not independent of location" is the alternative hypothesis (it states a relationship between the variables).
• "Skill level in a subject is related to location" is also an alternative - type statement (suggesting a relationship).
• "Cannot be determined" is incorrect as we can state the null hypothesis for the test.
• "Skill level in a subject is independent of location" matches the definition of the null hypothesis for a Chi - Square test of independence.

Answer:

E. Skill level in a subject is independent of location.