Question

1. A national equal employment opportunities committee is conducting an investigation to determine if women employees are as well paid as their male counterparts in comparable jobs. Random samples of 75 males and 64 females in junior academic positions are selected and their salary data is stored in “salaries.csv". (a) Find the mean and the standard deviation of each group. (b) Draw a boxplot of each group side by side and comment interpret what you observe from two box- plots). (c) Test whether there is a significant difference in the mean salaries of male and females in comparable jobs. Use a=0.1. (Follow all the necessary steps) (d) Find the 90% confidence interval for the difference between mean salaries of males and females in comparable jobs. Note that you can also make the same conclusion in (a) based on this confidence interval. (e) Test whether there is a significant gender bias against females in the mean salaries. Use a = 0.05. (Follow all the necessary steps)

gender	income
Male	48932
Male	48281
Male	49885
Male	48646
Male	49391
Male	48824
Male	49459
Male	48685
Male	48215
Male	49362
Male	47647
Male	48860
Male	47438
Male	47052
Male	48157
Male	48349
Male	49589
Male	48579
Male	48411
Male	49048
Male	48705
Male	49932
Male	48779
Male	47685
Male	48984
Male	48616
Male	47362
Male	46919
Male	47676
Male	47932
Male	48494
Male	49161
Male	48201
Male	48089
Male	48287
Male	48028
Male	48240
Male	48312
Male	47827
Male	47839
Male	48578
Male	49740
Male	48942
Male	49759
Male	48134
Male	47934
Male	47702
Male	46989
Male	48716
Male	49599
Male	48713
Male	49089
Male	48228
Male	48074
Male	48683
Male	48268
Male	47844
Male	49145
Male	49657
Male	49046
Male	47516
Male	48733
Male	48385
Male	47807
Male	49290
Male	47782
Male	48052
Male	49397
Male	49392
Male	48313
Male	47652
Male	48452
Male	48097
Male	47012
Male	48584
Female	46737
Female	48929
Female	47321
Female	47952
Female	47958
Female	47563
Female	47843
Female	46724
Female	46122
Female	48661
Female	47558
Female	47914
Female	46808
Female	48822
Female	48373
Female	47905
Female	47196
Female	46710
Female	46597
Female	46558
Female	47428
Female	46701
Female	47780
Female	47670
Female	48262
Female	47343
Female	48079
Female	46398
Female	47727
Female	47421
Female	47244
Female	48538
Female	47944
Female	47615
Female	48875
Female	46970
Female	48847
Female	46854
Female	47011
Female	47582
Female	47536
Female	48259
Female	48181
Female	47912
Female	47480
Female	48614
Female	47961
Female	47557
Female	47566
Female	46611
Female	47469
Female	47443
Female	47577
Female	46846
Female	46970
Female	48256
Female	47713
Female	47921
Female	48312
Female	48960
Female	47486
Female	47326
Female	48162
Female	48339

Do this by R and put the syntax of R and corresponding outputs under respective questions.

Answer 1

Enter the all value of male dataset and call as X and y respectively .I.e.

x= c( )

y =c( l

n1 = 75

n2 =64

a) mean (x) = 48469.93

Sd(x) = 722.077

mean(y)=47640.578

sd (y) = 678.096

b) boxplot(x)

boxplot(y)

50000 49800 49600 49400 49200 49000 48800 48600 48400 48200 48000 47800 47600 47400 47200 47000 46800

49000 日日DO 49600 48400。 日200 18000 47800 47600- 47400- 47200- 4700- 46800 400- E400- 46200- 000

INTERPRETATION :- By observing two boxplot , both dataset male and female are symmetrically distributed.

c) t.test(x,y)

t = 6.975 ,

d.f = 137

P value = 0.0000

t cal = n1+ n2 -2 ,0.01 = 2.612

Hypothesis :-

The following null and alternative hypotheses need to be tested:

Ho: Two means are equal.

Ha: Two means are different.

Here p < alpha , reject H0

Interpretation :- mean salaries of males and females are statistically different at 0.01 significance level.

d) confint (x,y ,alpha = 0.01)

The 99% confidence interval is

518.729<μ1​−μ2​<1139.975.

Conclusion :- we are 90% confident that the mean difference is lies between 518 729 and 1139.975