Question

The average testosterone level for men is 680 ng/dL. She wants to determine whether going to the gym is associated with increased testosterone levels. She studies 100 men: 50 regularly go to the gym and 50 do not. For each of these groups (gym, no gym), she determines how many have testosterone >680, and how many ≤680 ng/dL.

A Chi-square. B. 1-sample t-test C. 2-sample paired t-test D. 2-sample unpaired t-test E. F-test. D. None of the above

Answer 1

Since we have to find the association between 2 categorical variables (gym and testosterone levels), we use a chi square test of independence.

_______________________

To do the test we must ensure that the sampling is random and that subjects are independnt of each other. The expected cell frequency for each cell is at least 5.

Expected frequency is calculated as row total * column total   /N, where N is the total Observations

The degrees of freedom is given by (r - 1) * (c - 1), and we use this df to calculate p value or the critical rule and test the statistic for significance for the following Rejection Rules.

If Test is > c, then reject H0

If p value is < , Then Reject H0.

___________________________