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 = 0.05, test the claim that each agency charges the same hourly wage.
Agency A Agency B
X 1 = $9.55/hour X 2 = $9.25/hour

s1 = $1.45/hour s2 = $1.25/hour
n1 = 20 n2 = 18

The formula for the correlation coefficient r is?

Explanation / Answer

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate Hypothesis, There Is Significance between them - H1: u1 != u2
Test Statistic
X(Mean)=9.55
Standard Deviation(s.d1)=1.45 ; Number(n1)=20
Y(Mean)=9.25
Standard Deviation(s.d2)=1.25; Number(n2)=18
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =9.55-9.25/Sqrt((2.1025/20)+(1.5625/18))
to =0.685
| to | =0.685
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 17 d.f is 2.11
We got |to| = 0.68478 & | t | = 2.11
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 0.6848 ) = 0.503
Hence Value of P0.05 < 0.503,Here We Do not Reject Ho

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