Chapter 10, Problem 5PT

To determine

To find: The correct test statistics.

Answer to Problem 5PT

The correct outcome is shown by option (a)

Explanation of Solution

Given:

Sample size $\left(n_1\right)=60$

Sample mean $\left({\overline{x}}_1\right)=6$

Sample standard deviation $\left(s_1\right)=3$

Sample size $\left(n_2\right)=40$

Sample mean $\left({\overline{x}}_2\right)=5$

Sample standard deviation $\left(s_2\right)=2$

Formula used:

The formula to compute the test statistic is:

  $t=\frac{\left({\overline{x}}_1-{\overline{x}}_2\right)-\left({\mu }_1-{\mu }_2\right)}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$

Calculation:

The test statistic can be computed as:

  $\begin{array}{c}t=\frac{\left({\overline{x}}_1-{\overline{x}}_2\right)-\left({\mu }_1-{\mu }_2\right)}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\\ =\frac{\left(6-5\right)-\left(0\right)}{\sqrt{\frac{3^2}{60}+\frac{2^2}{40}}}\end{array}$

Hence, the correct option is (b).