Question

a random sample of 120 students were asked if they play a varsity sport. the results were sorted by gender. a chi - 2 test of independence will be performed to determine if there is evidence of an association between gender and sports participation for students at the school. which of the following is the correct null - hypothesis for this test?
ho: males at this school are more likely than females to play a varsity sport.
ho: there is an association between sports participation and gender.
ho: females at this school are more likely than males to play a varsity sport.
ho: there is no association between sports participation and gender.

Explanation:

Step1: Recall the definition of null hypothesis in chi - square test of independence

The null hypothesis \(H_0\) for a chi - square test of independence states that there is no association between the two categorical variables. In this case, the two categorical variables are gender and sports participation.

Step2: Analyze each option

• Option 1: "Males at this school are more likely than females to play a varsity sport" is an alternative - type statement (a claim of an association/difference), not a null hypothesis.
• Option 2: "There is an association between sports participation and gender" is an alternative hypothesis.
• Option 3: "Females at this school are more likely than males to play a varsity sport" is also an alternative - type statement.
• Option 4: "There is no association between sports participation and gender" is in line with the definition of the null hypothesis for a chi - square test of independence.

Answer:

The correct null - hypothesis for this test is "Ho: There is no association between sports participation and gender".