Chapter 10, Problem T10.5SPT

To determine

To find out which of the following is the correct test statistics.

Answer to Problem T10.5SPT

Option (e) is the correct test statistics.

Explanation of Solution

It is given in the question that:

  $\begin{array}{l}{n}_1=\text{Sample size=60}\\ n_2=\text{Sample size=40}\\ {\overline{x}}_1=\text{Mean=6}\\ {\overline{x}}_2=\text{Mean=5}\\ s_1=\text{Standard deviation=3}\\ s_2=\text{Standard deviation=2}\end{array}$

We are carrying a significance test for the mean difference,

  $H_0:{\mu }_{\text{suburban}}={\mu }_{\text{city}}$

Since we are carrying out the test for the mean, we use a t test statistic when carrying out a test for the proportion we use a z test statistics.

Now, the test statistics is as:

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

Thus the correct option is (e) option.