To compare the salaries of two firms A and B two independent

To compare the salaries of two firms, A and B, two independent random samples of employees were taken. The following represents the findings (in thousands).

Company

1

2

3

4

5

6

7

8

9

10

A

41.5

39

47

102

89

62.5

55

50

48

62

B

38

90

80

62

55

60

61

71

At the .01 significance level, determine whether there is a mean difference between the salaries A and B. (Assume that the two population variances are equal.)

Solution

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)=59.6
Standard Deviation(s.d1)=20.642 ; Number(n1)=10
Y(Mean)=64.625
Standard Deviation(s.d2)=15.873; Number(n2)=8
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =59.6-64.625/Sqrt((426.09216/10)+(251.95213/8))
to =-0.58
| to | =0.58
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 7 d.f is 3.499
We got |to| = 0.58374 & | t | = 3.499
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -0.5837 ) = 0.578
Hence Value of P0.01 < 0.578,Here We Do not Reject Ho