Consider the following hypothesis test:

$H_0:μ_1-μ_2=0$

$H_a:μ_1-μ_2≠0$

The following results are from independent sample taken from two populations:

What is the value of the test statistic?

2.18

The correct answer is Option (2) → 2.18

Given, $D_0 = 0, n_1 = 35, n_2 = 40, x_1 = 13.6, x_2 = 10.1, S_1 = 5.2$ and $S_2 = 8.5$

$t = \frac{(\bar{x}_1 - \bar{x}_2)-D_0}{\sqrt{\frac{S_1^2}{n_1} + \frac{S_2^2}{n_2}}} = \frac{(13.6 - 10.1)-0}{\sqrt{\frac{(5.2)^2}{35} + \frac{(8.5)^2}{40}}}$

$= \frac{3.5}{\sqrt{\frac{27.04}{35} + \frac{72.25}{40}}} = \frac{3.5}{\sqrt{0.77251 + 1.80625}} = \frac{3.5}{\sqrt{2.57876}}$

$= \frac{3.5}{1.6058}=2.18$

$∴t=2.18$