Mean entry level salaries for college graduates with mechani

Mean entry level salaries for college graduates with mechanical engineering degrees and electricalengineering degrees are believed to be approximately the same.(Source: http://www.graduatingengineer.com10). A recruiting oce thinks that the mean mechan-ical engineering salary is actually lower than the mean electrical engineering salary. The recruitingoce randomly surveys 50 entry level mechanical engineers and 60 entry level electrical engineers.Their mean salaries were $46, 100 and $46, 700, respectively. Their standard deviations were $3450and $4210, respectively. Conduct a hypothesis test to determine if you agree that the mean entrylevel mechanical engineering salary is lower than the mean entry level electrical engineering salary

Solution

To test H0:µ1>=µ2 vs H1:µ1<µ2(claim)
X1bar=46100
X2bar=46700

S1=3450
S2=4210
Assuming equality of variances we find out pooled variance
S^2={(50-1)*3450^2+(60-1)*4210^2}/{50+60-2}=15082818.52
S=3883.6605
The test statistic is
=(X1bar-X2bar)/(s*(1/n1+1/n2))
=(46100-46700)/(3883.6605*(1/50+1/60))
=-0.81
The t distribution has degrees of freedom (50+60-2) =108
It can be approximated to normal distribution.
The p value=0.20897.
So p value is >=0.05.
Hence we fail to reject the null hypothesis at 5% level of significance.
Conclusion: that the average entry level mechanical engineering salary is not lower than the average entry level electrical engineering salary.