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:

The p-value is;

d. 0.00131

Step-by-step explanation:

The given question parameters are;

                                                     Company A   [tex]{}[/tex]                       Company B

Sample size                                   80[tex]{}[/tex]                                         60

Sample mean   [tex]{}[/tex]                            [tex]\overline x_1[/tex] $16.75                            [tex]\overline x_2[/tex] $16.25

Population standard deviation [tex]{}[/tex]   σ₁  $1.00                           σ₂ $0.95

[tex]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}}}}[/tex]

Therefor, we have;

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

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

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