[tex] n_1=25, n_2=25\\ \bar{X_1}=35.5, \bar{X_2}=33\\ s_1=3, s_2=4
[/tex]
Pooled Combined Variance [tex] s_p=12.5 [/tex]
Test Statistic:
[tex] t=\frac{\left(\bar{X_1}-\bar{X_2}\right)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} [/tex]
[tex] t=\frac{\left(35.5-33\right)}{12.5\sqrt{\frac{1}{25}+\frac{1}{25}}} [/tex]
[tex] \left|t\right|=0.01414 [/tex]
Degrees of freedom = [tex] n_1+n_2-2=25+25-2=48 [/tex]
[tex] \alpha =0.05 [/tex]
[tex] t-Critical =t_{\alpha /2, n_1+n_2-2}=t_{0.025, 48}=-2.0206
\\Table value=|t|=2.0206\\|t|=2.0206<0.01414
[/tex]
The table value is greater than the calculated value.
Thus we accept H0.
