Question

question 18 (1 point)
what is the formula for t for the paired samples t - test?
$t = \frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}$
$t = \frac{\overline{x}-\mu_{d}}{\frac{s}{\sqrt{n}}}$
$t = \frac{\overline{x}_{1}-\overline{x}_{2}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}$
none is correct

Explanation:

Step1: Recall the formula for paired samples t - test

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

Step2: Analyze the given options

• The formula \(t = \frac{\bar{x}-\mu}{s/\sqrt{n}}\) is for one - sample t - test.
• The formula \(t=\frac{\bar{x}_d - 0}{s/\sqrt{n}}\) is not a standard formula for paired samples (the correct formula has the standard deviation of differences \(s_d\) not \(s\)).
• The formula \(t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\) is for independent samples t - test (assuming unequal variances).

Answer:

none is correct