A study was performed to examine the personal goals of children in grades 4,5,and 6.A random sample of students was selected from each of the grades 4,5,and 6 from schools in Georgia.The students received a questionnaire regarding achieving personal goals.They were asked what they would most like to do at school: make good grades,be good at sports,or be popular.Results are presented by the gender of the child in the table below. What would be the null hypothesis for a chi-square test based on these data?

Question

A study was performed to examine the personal goals of children in grades 4,5,and 6.A random sample of students was selected from each of the grades 4,5,and 6 from schools in Georgia.The students received a questionnaire regarding achieving personal goals.They were asked what they would most like to do at school: make good grades,be good at sports,or be popular.Results are presented by the gender of the child in the table below.  What would be the null hypothesis for a chi-square test based on these data?

Quizplus · Accepted Answer

The null hypothesis for a chi-square test of independence states that the two variables being tested (in this case, personal goals and gender) are independent of each other. This means that there is no association between the two variables and that any differences in personal goals between boys and girls can be explained by chance. Choice B is not appropriate because it refers to a mean rather than a distribution, and choice C is incorrect because it suggests that there is a difference in the distributions of personal goals between boys and girls, when in fact the goal is to test whether there is an association between personal goals and gender. Choice D is not relevant because it refers to the distribution of gender, which is not the variable of interest in this study.

A Study Was Performed to Examine the Personal Goals of Children