Question

to test the effectiveness of a new treatment, a clinician measures cholesterol levels (in mg/dl) of 9 patients before and after treatment. the mean difference is 12, and the standard deviation of the differences is 6. what is the test statistic (t) for this test

1

2

6

12

Explanation:

Step1: Recall the formula for the t - statistic in a paired - t test

The formula for the t - statistic in a paired - t test is \(t=\frac{\bar{d}}{s_d/\sqrt{n}}\), where \(\bar{d}\) is the mean difference, \(s_d\) is the standard deviation of the differences, and \(n\) is the number of pairs.

Step2: Substitute the given values into the formula

We are given that \(\bar{d} = 12\), \(s_d=6\), and \(n = 9\).
First, calculate \(\sqrt{n}=\sqrt{9}=3\).
Then, calculate \(s_d/\sqrt{n}=\frac{6}{3}=2\).
Finally, calculate \(t=\frac{\bar{d}}{s_d/\sqrt{n}}=\frac{12}{2}\).

Answer:

\(6\) (the third option)