Question

Exhibit B In order to determine whether or not there is a significant difference between the hourly wages of two companies, two independent random samples were selected and the following statistics were calculated. Company A Company B Sample size 80 60 Sample mean $6.75 $6.25 Population standard deviation $1.00 $0.95 Refer to Exhibit B. The value of the test statistic is _____.
a. 2.75
b. 0.098
c. 3.01
d. 1.645

Answer 1

Answer: c. 3.01

Step-by-step explanation:

The test statistic for difference between two population mean (when population standard deviation is known) is given by :

$z=\dfrac{\overline{x}_1-\overline{x}_2}{\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}}$

, where $n_1$ = Size of first sample

$n_2$ = Size of second sample

$\overline{x}_1-\overline{x}_2$ = Difference between two sample mean.

$\sigma_1$ = standard deviation for population 1.

$\sigma_2$ = standard deviation for population 2.

As per given , we have

$n_1=80$

$n_2=60$

$\overline{x}_1=\ 6.75$

$\overline{x}_2=\ 6.25$

$\sigma_1=\ 1$

$\sigma_2=\ 0.95$

Substitute these values in formula , we get

$z=\dfrac{6.75-6.25}{\sqrt{\dfrac{(1)^2}{80}+\dfrac{(0.95)^2}{60}}}$

$z=\dfrac{0.50}{\sqrt{0.0275416666667}}$

$z=\dfrac{0.50}{0.165956821694}$

$z=3.0128318613\approx3.01$

Hence, the value of the test statistic is 3.01.

Hence, the correct option is c. 3.01 .