Question

question 18 (1 point) what is the formula for t for the paired samples t - test? $t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$ $t = \frac{\overline{x_d} - 0}{\frac{s}{\sqrt{n}}}$ $t = \frac{\overline{x_1} - \overline{x_2}}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$ none is correct

Explanation:

Step1: Recall paired samples t - test formula

The formula for the paired samples t - test is \(t=\frac{\bar{x}_d - 0}{\frac{s_d}{\sqrt{n}}}\), where \(\bar{x}_d\) is the mean of the differences, \(s_d\) is the standard deviation of the differences, and \(n\) is the number of pairs.

Step2: Analyze given options

• The first option \(t = \frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\) is the formula for a one - sample t - test.
• The second option \(t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\) is the formula for an independent samples t - test.

Answer:

none is correct