Question

In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated.
Company A Company B
Sample size 80 60
Sample mean $16.75 $16.25

Population standard deviation $1.00 $.95 The p-value is:_________

a. 0.0084.
b. 0.0042.
c. 0.0026.
d. 0.0013

Answer 1

Answer:

The p-value is;

d. 0.00131

Step-by-step explanation:

The given question parameters are;

                                                     Company A   ${}$                       Company B

Sample size                                   80${}$                                         60

Sample mean   ${}$                            $\overline x_1$ $16.75                            $\overline x_2$ $16.25

Population standard deviation ${}$   σ₁  $1.00                           σ₂ $0.95

$z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}+\dfrac{\sigma _{2}^{2}}{n_{2}}}}$

Therefor, we have;

$z=\dfrac{(16.75-16.25)-(0-0)}{\sqrt{\dfrac{1^{2} }{80}+\dfrac{0.95^{2}}{60}}} \approx 3.0128$

The p-value = 1 - 0.99869 (the area to the right of 3.01) = 0.00131