Question

1.) Problem: You are applying for jobs after graduating and are looking at a particular company. You've heard that they don't pay women as much as men starting out and want to test it at the p<.01 level before deciding to work there. Luckily you are able to get publicly available salary information and randomly select the starting salary of 7 women and 6 men to see if women are paid less than men at this company. The salaries of the 7 women are: 45k, 48k, 50k, 42k, 46k, 51k, 43k. The salaries of the 6 men are: 46k, 48k, 52k, 49k, 47k, 51k. a. Restate the question: • Population 1: • Population 2 (comparison): • Research hypothesis: • Null hypothesis: b. Determine the characteristics of the comparison distribution to compare to sample distribution: • Ma(Mean, Sample 1): • SS (Sum of squares, Sample 1): • dfi (degrees of freedom, Sample 1): • S (estimated variance, Population 1): • M2(Mean, Sample 2): • SS (Sum of Squares, Sample 2):

Answer 1

POPULATION 1: SALARIED WOMEN

POPULATION 2: SALARIED MED

RESERACH HYPOTHEIS Ha: Average income of salried women is less than Average income of salaried men.

HA: $\mu1< \mu 2$ LEFT TAILED TEST.

NULL HYPOTHESIS H0: Average income of salaried women is equal to average income of salried men.

H0: $\mu1= \mu 2$

b]

WOMEN (SAMPLE 1) MEN SAMPLE 2) 49 51 MEAN SD VARIANCE 43 46.42857143 3.408672413 11.61904762 48.83333333 MEAN 2.316606714 SD 5.366666667 VARIANCE

DF1= 7-1=6

DF2= 6-1=5

DF (TOTAL)= n1+n2-1= 7+6-2= 11

s^2 pooled variance= ((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2)= 7*11.62+5*5.37/11= 8.78915

POOLED STANDARD DEVIATION= SQRT(8.78915)= 2.965

STANDARD ERROR OF DIFFERENCE= 1.645

WHEN VARIANCES ARE EQUAL 7 Pooled Variance= 3.41 S.D 6 S.E 2.32 s112 46.43 s2^2 48.83 DIFFERENCE OF MEANS 8.78915 2.96465 1.64938 11.6281 5.3824 - -2.4 MEAN 1 MEAN 2 DEGREES OF FREEDOM I TEST STATISTIC 11 -1.455093447

t score= DIFFERENCE OF MEANS/STANDARD ERROR OF DIFFERENCE

t score= -2.4/1.65

t score= -1.455

LEVEL OF SIGNIFICANCE =0.01

t critical value= -2.718

Since t critical statistic SMALLER THAN t cal for left tailed test therefore NOT SIGNIFICANT

DECISION: DO NOT REJECT H0.

CONCLUSION:WE DO NOT HAVE SUFFICIENT EVIDENCE TO SHOW THAT Average income of salried women is less than Average income of salaried men at 0.01