Question

Finger length Is your index finger longer than your ring finger? Or is it the other way around? It isn't the same for everyone. To investigate if there is a relationship between gender and relative finger length, we selected a random sample of $460$U.S. high school students who completed a survey. The two-way table shows the results.

Do these data provide convincing evidence at the $\alpha =0.10$level of an association between gender and relative finger length in the population of students who completed the survey?

Short answer

No, the data is not convincing evidence at the level of an association.

Step-by-step solution

Given information

We need to find out whether the data provided is convincing evidence or not.

Explanation

We know that

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

$H_0$is there is no association between gender and relative finger length.

$H_{\alpha }$is there is an association between gender and relative finger length.

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, the data is not convincing evidence at the level of an association.