Statistics for Management

Statistics for Management

Activity 1
Mean earnings in public sector
Mean
Earnings:
in £
2009 2010 2011 2012 2013 2014 2015 2016
Men 30638 31264 31380 31816 32541 32878 33685 34011
Women 25224 26113 26470 26663 27338 27705 27900 28053
a) Hypothesis: Earning of men in public sector is not significantly different to the earnings of
women in public sector
Testing hypothesis at 5% level of significance
H0: Men ≠ Women
H1: Men = Women
Sample size Average earnings Standard deviation
Men 1000 32276.63 1204.144
Women 1000 26933.25 987.7715
Using t-distribution test, p-value at 1000 degrees of freedom
__ __
t = X1 – X2 .
√ (N1 – 1) s12 + (N2 – 1) s22 ) (1 + 1)
N1 + N2 – 2 N1 N2
= 32276.63 – 26933.25 .
√ (1000 – 1) 12042 + (1000 – 1) 9882 ) (1 + 1)
1000 + 1000 – 2 1000 1000
= 242.88
at 1998 degrees of freedom testimated value at 5% level of significance is 1.646
so, tcal > test. there, hypothesis is rejected therefore, earning of men in public sector is significantly
different to the earnings of women in public sector
1

b)
Mean earnings in private sector
Mean
Earnings:
in £
2009 2010 2011 2012 2013 2014 2015 2016
Men 27632 27000 27233 27705 28201 28442 28881 29679
Women 19551 19532 19565 20313 20698 21017 21403 22251
Hypothesis: Earning of men in public sector is not significantly different to the earnings of
women in private sector
Testing hypothesis at 5% level of significance
H0: Men ≠ Women
H1: Men = Women
Sample size Average earnings Standard deviation
Men 1000 28096.625 891.7890426
Women 1000 20541.25 994.3489974
Using t-distribution test, p-value at 1000 degrees of freedom
__ __
t = X1 – X2 .
√ (N1 – 1) s12 + (N2 – 1) s22 ) (1 + 1)
N1 + N2 – 2 N1 N2
= 28096.625 – 20541.25 .
√ (1000 – 1) 8922 + (1000 – 1) 9942 ) (1 + 1)
1000 + 1000 – 2 1000 1000
= 178.91
at 1998 degrees of freedom testimated value at 5% level of significance is 1.646
so, tcal > test. there, hypothesis is rejected therefore, earning of men in private sector is
significantly different to the earnings of women in public sector
c)
2