The Donaldson Corporation wants to hire a temporary secretary. There are two emp

Question

The Donaldson Corporation wants to hire a temporary secretary. There are two employment agencies in town, and it is believed that the average hourly wage charged by both agencies is the same. A Donaldson manager surveyed other employers in town to find what they paid the agencies for temporary secretaries. The results are summarized below. At ? = .05, test the claim that each agency charges the same hourly wage. Show the answers to the 5 steps of the hypothesis test.


Agency A Agency B
X1= $9.25 / hr x2= 9.55/hr
s1 = 1>25/ hr s2 = $1.45/ hr
n1=18 n2 = 20

Explanation / Answer

The test hypothesis is
Ho:1=2
Ha:1 not equal to 2

The test statistic is

t=(xbar1 -xbar2)/[s1^2/n1 + s2^2/n2]

=(9.25-9.55)/sqrt(1.25^2/18 + 1.45^2/20)

= -0.68

Given a=0.05, the critical value is t(0.025, df=n1+n2-2=18+20-2=36) =-2.03 (check student t table)

Since t=-0.68 > -2.03, we do not reject Ho.

So we can conclude that each agency charges the same hourly wage

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