Question

Popular kids Who were the popular kids at your elementary school? Did they get good grades or have good looks? Were they good at sports? A study was performed in Michigan to examine the factors that determine social status for children in grades $4,5,$and $6$. Researchers administered a questionnaire to a random sample of $478$students in these grades. One of the questions asked, "What would you most like to do at school: make good grades, be good at sports, or be popular?" The two-way table summarizes the students' responses. Is there convincing evidence of an association between gender and goal for students in grades $4,5,$and $6$?

Short answer

Yes, there is a piece of convincing evidence for the association between goals and gender.

Step-by-step solution

Given information

We need to find out whether there is convincing evidence for the given data or not.

Explanation

We know that

The null hypothesis asserts that the variables are unrelated, whereas the alternative hypothesis asserts that they are.

$H_0$represents there is an association between goals and gender.

$H_{\alpha }$ represents there is no association between goals and gender.

And expected frequencies are a product of row and column total divided by table total.

And The squared differences between the actual and predicted frequencies, divided by the expected frequency, make up the chi-square subtotals.

Therefore, there is a piece of convincing evidence for the association between goals and gender.