Find the standardized test statistic, t, to test the hypothesis that μ1

Question

Find the standardized test statistic, t, to test the hypothesis that μ1 < μ2. Two samples are randomly selectedand come from populations that are normal. The sample statistics are given below. $$\begin{array}{l}
\mathrm { n } _ { 1 } = 15 \quad \mathrm { n } _ { 2 } = 15\
\bar { x } 1 = 27.44 \quad \bar { x } 2 = 29.99\
\mathrm { s } _ { 1 } = 2.9 \quad \mathrm {~s} _ { 2 } = 2.8
\end{array}$$
A) -2.450
B) -3.165
C) -1.667
D) -0.669

Quizplus · Accepted Answer

The standardized test statistic, $t$, can be calculated using the formula for two independent samples:$$ t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} $$Given:- $n_1 = n_2 = 15$- $\bar{x}_1 = 27.44$, $\bar{x}_2 = 29.99$- $s_1 = 2.9$, $s_2 = 2.8$Plugging the values into the formula:$$ t = \frac{27.44 - 29.99}{\sqrt{\frac{2.9^2}{15} + \frac{2.8^2}{15}}} \approx -2.450 $$Therefore, the correct answer is -2.450, which corresponds to choice A.

Find the Standardized Test Statistic, T, to Test the Hypothesis