Data is gathered from two groups resulting in the following sets of data:

Group 1: $\left[2\, 2\, 4\, 5\, 6\, 7\, 8\, 9\, 5\, 6\right]$

Group 2: $\left[5\, 4\, 5\, 6\, 7\, 8\, 9\,5\, 9\, 5\right]$

Assuming a significance level of 5% (two-sided test), are the means of the two sets of data significantly different?

The following hypotheses are tested when a two sample t-test is applied:

H₀ : the true population means are equal

H_a : the true population means differ

The t-test statistic is calculated in the following manner:

First, the mean and variance for each of the groups are computed:

Substituting this into the formula for the t-test statistic gives:

$t\=\frac{5.4-6.3}{\sqrt{\frac{5.378}{10}\+\frac{3.344}{10}}}$

$t\=-0.964$

From a critical t-table, it can be observed that the critical value is $t_{18\;\frac{0.05}{2}}\=2.101$.

Since $\mathrm{abs}\left(t\right)\&equals;0.963<t_{18\&semi;0.025}\&equals;2.101$, the null hypothesis cannot be rejected. Therefore, it can be concluded that the population means of the two groups do not differ significantly.