Question

Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. the first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. the pooled estimate of the common variance is 12.5. what is the value of the computed test statistic for testing the equality of the population means

Answer 1

$n_1=25, n_2=25\\ \bar{X_1}=35.5, \bar{X_2}=33\\ s_1=3, s_2=4$

Pooled Combined Variance $s_p=12.5$

Test Statistic:

$t=\frac{\left(\bar{X_1}-\bar{X_2}\right)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

$t=\frac{\left(35.5-33\right)}{12.5\sqrt{\frac{1}{25}+\frac{1}{25}}}$

$\left|t\right|=0.01414$

Degrees of freedom = $n_1+n_2-2=25+25-2=48$

$\alpha =0.05$

$t-Critical =t_{\alpha /2, n_1+n_2-2}=t_{0.025, 48}=-2.0206 \\Table value=|t|=2.0206\\|t|=2.0206$

The table value is greater than the calculated value.

Thus we accept H0.