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. $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \
\overline { \mathrm { x } } 1 = 2.8 & \overline { x } _ { 2 } = 3.2 \
\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 0.51
\end{array}$$

A) -1.546
B) -1.821
C) -2.123
D) -1.326

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. $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \
\overline { \mathrm { x } } 1 = 2.8 & \overline { x } _ { 2 } = 3.2 \
\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 0.51
\end{array}$$

A) -1.546
B) -1.821
C) -2.123
D) -1.326

Quizplus · Accepted Answer

The t-statistic is calculated using the formula for two independent samples: $ t = \frac{(\overline{x}_1 - \overline{x}_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} $. Substituting the given values results in approximately -1.546.

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