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

Option d - 2.7

Explanation:

To find : The test statistic has a value ?

Solution :

Using test statistic formula,

`Z_0=\frac{\bar{y_1}-\bar{y_2}}{\sqrt{(\sigma_1^2)/(n_1)+(\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{(2^2)/(80)+(1.50^2)/(60)}}`

`Z_0=\frac{0.8}{\sqrt{(4)/(80)+(2.25)/(60)}}`

`Z_0=(0.8)/(√(0.05+0.0375))`

`Z_0=(0.8)/(√(0.0875))`

`Z_0=(0.8)/(0.2958)`

`Z_0=2.70`

Therefore, The test statistic has a value of 2.7.

So, Option d is correct.