A researcher wanted to determine whether gender differences exist in job satisfa
ID: 3203920 • Letter: A
Question
A researcher wanted to determine whether gender differences exist in job satisfaction for middle aged adults. Nine middle aged women and nine middle aged men were asked to rate their job satisfaction on a scale of 0 (totally dissatisfied) to 10 (totally satisfied). Perform an independent t-test on the data below to determine the outcome (alpha = .05, two-tailed):
Females (n = 9)
Males (n = 9)
6
8
7
7
7
9
6
7
5
6
8
8
6
10
7
8
7
9
In the box below, provide the following information:
Null Hypothesis in sentence form (1 pt.):
Alternative Hypothesis in sentence form (1 pt.):
Critical Value(s) (2 pts.):
Outcome (determination of significance or not significant, 2 pts.):
Calculations (4 pts.):
Females (n = 9)
Males (n = 9)
6
8
7
7
7
9
6
7
5
6
8
8
6
10
7
8
7
9
Explanation / Answer
A.a)Null Hypothesis (Null Hypothesis always implies there is no change in the existing situation)
H0: There is no Gender Difference existing in job satisfaction of middle age adults
H0: µ1=µ2
A.b)Alternate Hypothesis (Alternate Hypothesis always implies there is a change in the existing situation)
H1: There is a Gender Difference existing in job satisfaction of middle age adults
H1: µ1µ2
A.c) =0.05
Df=n1+n2-2=9+9-2=16
Critical value from the t-table is 2.12
A.e) we need to calculate the t-statistic
From the table we get
Mean of female(x1)=6.56
Mean of male(x2)=8
SD of female(SD1)=0.88
SD of male(SD2)=1.22
Df1=9-1=8
Df2=9-1=8
We need to calculate the estimated standard error of difference
Standard error of difference SE(d)=(df1*sd1*sd1+df2*sd2*sd2)/(df1+df2)
SE(d)=(8*0.88*0.88+8*1.22*1.22)/(8+8)
SE(d)=1.5186
Now, Standard error(SE)=Sqrt[SE(d)/n1+SE(d)/n2]
SE=Sqrt(0.338)=0.58
Hence standard error is 0.58
Now t-statistic is
t = (x1-x2)/SE
t=(6.56-8)/0.58
t=-2.47
A.d) t(calc)=-2.47
t()=2.12
which means the acceptable region/range is between -2.12 to +2.12
as t(calc) is beyond the acceptable region of t(), we shall reject the null hypothesis or accept the alternate hypothesis
hence we can conclude that There is a Gender Difference existing in job satisfaction of middle age adults
in other words the gender difference for a job satisfaction of middle age adults is significant
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