the correlation coefficient
david1962
hypothesis_testing-hr_salary_for_directors.docCALCULATE T TEST
Calculate the “t” value for independent groups for the following data using the formula provided in the attached word document. Using the raw measurement data presented, determine whether or not there exists a statistically significant difference between the salaries of female and male human resource managers using the appropriate t-test. Develop a testable hypothesis, confidence level, and degrees of freedom. Report the required “t” critical values based on the degrees of freedom. Show calculations.
Answer
The null hypothesis tested is
H0: There is no significant difference between the average salaries of female and male human resource managers. (µ1= µ2)
The alternative hypothesis is
H1: There is significant difference between the average salaries of female and male human resource managers. (µ1≠ µ2)
The test statistic used is
12
12
2
~
NN
DM
MM
tt
S
+-
-
=
Where22
1122
1212
(1)(1)
11
2
DM
NsNs
S
NNNN
éùéù
-+-
=+
êúêú
+-
ëûëû
Here M1 = 62,200, M2 = 63,700
s1 = 9330.95, s2 = 6912.95
N1 = 10, N2 = 10 (See the excel sheet)
Then,
(
)
(
)
22
(101)9330.95(101)6912.95
11
101021010
DM
S
éù
-+-
éù
=+
êú
êú
+-
ëû
êú
ëû
= 3672.267768Therefore test statistic,
62,20063,700
3672.267768
t
-
=
= -0.408466946Degrees of freedom = N1 + N2 – 2 = 10 + 10 – 2 = 18
Let the significance level be 0.05.
Rejection criteria: Reject the null hypothesis, if the calculated value of t is greater than the critical value of t at 0.05 significance level.
The critical values can be obtained from the student’s t tables with 18 d.f. at 0.05 significance level.
Upper critical value = 2.1
Lower critical value = -2.1
0
.
4
0
.
3
0
.
2
0
.
1
0
.
0
X
D
e
n
s
i
t
y
-
2
.
1
0
0
.
0
2
5
2
.
1
0
0
.
0
2
5
0
D
i
s
t
r
i
b
u
t
i
o
n
P
l
o
t
T
,
d
f
=
1
8
Conclusion: Fails to reject the null hypothesis. The sample does not provide enough evidence to support the claim that there is significant difference between the salaries of female and male human resource managers.
