A study examines the personal goals of children in grades 4, 5, and 6. A random sample of students was selected for each of the grades 4, 5, and 6 from schools in Georgia. The students received a questionnaire regarding achievement of 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 in the following table by the sex of the child.

Boys Girls

Make good grades 96 295

Be popular 32 45

Be good in sports 94 40

Which hypotheses are being tested by the chi-square test?

a. The null hypothesis is that personal goals and gender are independent, and the alternative is that they are dependent.

b. The null hypothesis is that the mean personal goal is the same for boys and girls, and the alternative is that the means differ.

c. The distribution of personal goals is different for boys and girls.

d. The distribution of gender is different for the three different personal goals.