Question

(a) a study was performed to examine the personal goals of children in primary school. a random sample of students was selected from schools in ontario. 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. each student's gender was also recorded. which hypotheses are being tested by the chi-square test?

Answer 1

In a study examining the personal goals of children, a chi-square test could be used to test if there's a significant association between students' goals (academics, sports, popularity) and their gender, comparing observed to expected frequencies.

Step-by-step explanation:

The chi-square test is a statistical test used to determine if there is a significant association between categorical variables. In the context of the provided question, where students are asked about their personal goals at school and their gender is recorded, the null hypothesis for a chi-square test of independence would state that there is no association between the categorical variables in question: student goals (academic achievement, athletic success, or popularity) and gender.

For each goal, one would compare observed frequencies of responses from each gender with expected frequencies, assuming there's no relationship between the variables. If the chi-square test yields a test statistic with a corresponding p-value below a chosen significance level, then the null hypothesis would be rejected, indicating a significant relationship between gender and personal goals.