Question

In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated.Company A Company BSample size 80 60Sample Mean $10.80 $10.00Population Standard Deviation $2.00 @1.50Refer to Exhibit 10-13. The test statistic has a value of:a. 1.96b. 0.80c. 1.645d. 2.7

Answer 1

Answer:

Option d - 2.7

Step-by-step explanation:

To find : The test statistic has a value ?

Solution :

Using test statistic formula,

$Z_0=\frac{\bar{y_1}-\bar{y_2}}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}$

Where,

$\bar{y_1}=10.8$ is the sample mean of company A

$\bar{y_2}=10$ is the sample mean of company B

$\sigma_1=2$ is the standard deviation of company A

$\sigma_2=1.50$ is the standard deviation of company B

n= 80 is the sample size of company A

n= 60 is the sample size of company B

Substitute all the values in the formula,

$Z_0=\frac{10.8-10}{\sqrt{\frac{2^2}{80}+\frac{1.50^2}{60}}}$

$Z_0=\frac{0.8}{\sqrt{\frac{4}{80}+\frac{2.25}{60}}}$

$Z_0=\frac{0.8}{\sqrt{0.05+0.0375}}$

$Z_0=\frac{0.8}{\sqrt{0.0875}}$

$Z_0=\frac{0.8}{0.2958}$

$Z_0=2.70$

Therefore, The test statistic has a value of 2.7.

So, Option d is correct.