Data is gathered from two groups resulting in the following sets of data:
Group 1: $\left[2\,2comma;4comma;5comma;6comma;7comma;8comma;9comma;5comma;6\right]$
Group 2: $\left[5\,4comma;5comma;6comma;7comma;8comma;9comma;5comma;9comma;5\right]$
Assuming a significance level of 5% (twosided test), are the means of the two sets of data significantly different?
The following hypotheses are tested when a two sample ttest is applied:
H_{0} : the true population means are equal
H_{a} : the true population means differ
The ttest statistic is calculated in the following manner:
First, the mean and variance for each of the groups are computed:
Group 1:
Mean = 5.4
Variance = 5.378

Group 2:
Mean = 6.3
Variance = 3.344



Substituting this into the formula for the ttest statistic gives:
$t\=\frac{5.46.3}{\sqrt{\frac{5.378}{10}\+\frac{3.344}{10}}}$
$t\=0.964$
From a critical ttable, it can be observed that the critical value is ${t}_{18\;\frac{0.05}{2}}\=2.101$.
Since $\mathrm{abs}\left(t\right)\=0.963<{t}_{18\;0.025}\=2.101$, the null hypothesis cannot be rejected. Therefore, it can be concluded that the population means of the two groups do not differ significantly.