Case Study


Compensation For ID Professionals








o We used descriptive statistics to summarize the data in this case which is as follows:
SUMMARY STATISTICS





Salary($) Position Experience





Mean 3.99255E4 0.475 1.00833


Median 3.64895E4 0 1


Mode 2.84640E4 0 1


Standard Deviation 1.07934E4 0.499375 0.811335


Range 4.01090E4 1 2


Maximum 6.37300E4 1 2


Variance 1.16498E8 0.249375 0.658264


Sample Variance 1.17477E8 0.251471 0.663796


Sample Standard Dev. 1.08387E4 0.501468 0.814736


Sum 4.79106E6 57 121


Minimum 2.36210E4 0 0


Sum Of Squares 2.05265E11 57 201


Coeff Of Skewness 4.80722E-1 0.100125 -0.015211


Valid Observations 1.20000E2 120 120


2. At a 95% confidence interval, we determined that of the mean annual salary internal estimate for all salespersons contains and upper limit of $41884.6 and a lower limit of $37966.3. This estimate does not consider experience or the position of the sales people.


CONFIDENCE INTERVAL MEAN


X = Salary($)





SAMPLE MEAN OF X = 3.99255E4


SAMPLE VARIANCE OF X = 1.17477E8


SAMPLE SIZE OF X = 1.20000E2


CONFIDENCE = 9.50000E1





% CONFIDENCE = 95


D. F. = 119


t = 1.9801


SD. ERROR = 989.431


t*SD. ERROR = 1959.17


UPPER LIMIT = 41884.6


SAMPLE MEAN OF X = 39925.5


LOWER LIMIT = 37966.3





3 At a 95% confidence interval, we determined that of the mean annual salary internal estimate for all outside salespersons contains and upper limit of $50877.2 and a lower limit of $46783.7. The national value reported by Industrial Distribution reported that the typical outside salesperson made $50,000 in 1997. Their average of $50,000 is within the confidence interval that we have established and very close to the sample mean of $48,830.


CONFIDENCE INTERVAL MEAN


X = Var1


SAMPLE MEAN OF X = 4.88304E4


SAMPLE VARIANCE OF X = 6.27733E7


SAMPLE SIZE OF X = 6.00000E1


CONFIDENCE = 9.50000E1


% CONFIDENCE = 95


D. F. = 59


t = 2.001


SD. ERROR = 1022.85


t*SD. ERROR = 2046.72


UPPER LIMIT = 50877.2


SAMPLE MEAN OF X = 48830.4


LOWER LIMIT = 46783.7



o At a 95% confidence interval, we determined that of the mean annual salary internal estimate for all inside salespersons contains and upper limit of $31947.9 and a lower limit of $30093.2. The national value reported by Industrial Distribution reported that the typical inside salespersons made $30,000 in 1997. There average of $30,000 is very close to being in our confidence interval.
CONFIDENCE INTERVAL MEAN


X = Var1





SAMPLE MEAN OF X = 3.10205E4


SAMPLE VARIANCE OF X = 1.28869E7


SAMPLE SIZE OF X = 6.00000E1


CONFIDENCE = 9.50000E1





% CONFIDENCE = 95


D. F. = 59


t = 2.001


SD. ERROR = 463.445


t*SD. ERROR = 927.35


UPPER LIMIT = 31947.9


SAMPLE MEAN OF X = 31020.5


LOWER LIMIT = 30093.2














5. At the 95% confidence interval the estimate of the mean difference between the annual salary for outside salespersons and the mean annual salary for inside salespersons contains an upper limit of $20078.75 and lower limit of $15541.2


This estimate ignores the years of experience. From this confidence interval we can see, that the years of experience play a big role in determining salary for both inside and outside salespersons, because the confidence interval without the years of experience shows smaller values both in lower and upper limits than the confidence intervals, which have the years of experience included.


CONFIDENCE INTERVAL MEAN


X = Var1





SAMPLE MEAN OF X = 1.78099E4

SAMPLE VARIANCE OF X = 7.71316E7
SAMPLE SIZE OF X = 6.00000E1


CONFIDENCE = 9.50000E1





% CONFIDENCE = 95


D. F. = 59


t = 2.001


SD. ERROR = 1133.81


t*SD. ERROR = 2268.75


UPPER LIMIT = 20078.7


SAMPLE MEAN OF X = 17809.9


LOWER LIMIT = 15541.2





6. Using single factor ANOVA, we used the following hypothesis test to determine if there were any significant changes differences due to position.


Hypothesis


Ho: µ1 = µ2 =


Ha: at least one is different


Test Statistic: F Test


Decision Rule: Reject Ho if F > Fcrit or if P < alpha


Conclusion:


We rejected Ho because p-value= 4.96486E-31 < alpha and we therefore conclude that there is a difference between salaries due to a difference in positions.








Because there is a difference, we also conducted the Kruskal-Wallis Test. The hypothesis we used is below:





Hypothesis


Ho: all populations are identical


Ha: not all populations are identical


Test Statistic: Chi Squared


Decision Rule: Reject Ho if p <.05


Conclusion:


We rejected Ho because P-VALUE = 3.55031E-20 < alpha. Therefore we would conclude that there is a difference between populations. Furthermore, our opinions about differences don’t change between single factor Anova and the