Two-Sample Tests Math Example 4

Solution

1. 1
   SE: $\sqrt{\frac{15^2}{20} + \frac{20^2}{20}} = \sqrt{\frac{225}{20} + \frac{400}{20}} = \sqrt{11.25 + 20} = \sqrt{31.25} \approx 5.59$
2. 2
   t-statistic: $t = \frac{100-95}{5.59} = \frac{5}{5.59} \approx 0.895$
3. 3
   Welch's df: $df = \frac{(s_1^2/n_1 + s_2^2/n_2)^2}{\frac{(s_1^2/n_1)^2}{n_1-1}+\frac{(s_2^2/n_2)^2}{n_2-1}} = \frac{(31.25)^2}{\frac{11.25^2}{19}+\frac{20^2}{19}} \approx \frac{976.6}{6.67+21.05} \approx 35.2$
4. 4
   With df≈35 and t≈0.895, p-value > 0.05; fail to reject H₀