BUS308 Week 4 and Week 5 Employee Salary (New Questions)

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Week 4Confidence Intervals and Chi Square  (Chs 11 - 12)         
For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements.  Use .05 for your significance level in making your decisions.   
For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed.     
                
1Using our sample data, construct a 95% confidence interval for the population's mean salary for each gender.       
 Interpret the results.  How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)?   
  MeanSt error t value Low to High       
 Males              
 Females              
 <Reminder: standard error is the sample standard deviation divided by the square root of the sample size.>    
Interpretation:               
                
                
2Using our sample data, construct a 95% confidence interval for the mean salary difference between the genders in the population.      
  How does this compare to the findings in week 2, question 2?        
                
 DifferenceSt Err.T value  Low to High       
                
                
                
    Yes/No           
 Can the means be equal? Why?          
                
 How does this compare to the week 2, question 2 result (2 sampe t-test)?       
                
a.Why is using a two sample tool (t-test, confidence interval) a better choice than using 2 one-sample techniques when comparing two samples? 
                
                
3We found last week that the degrees compa values within the population.       
  do not impact compa rates.  This does not mean that degrees are distributed evenly across the grades and genders.    
 Do males and females have athe same distribution of degrees by grade?        
 (Note: while technically the sample size might not be large enough to perform this test, ignore this limitation for this exercise.)   
                
 What are the hypothesis statements:           
 Ho:               
 Ha:              
Note:  You can either use the Excel Chi-related functions or do the calculations manually.        
 Data input tables - graduate degrees by gender and grade level        
OBSERVEDA BCDEFTotal Do manual calculations per cell here (if desired)  
M Grad        A BCDEF 
Fem Grad       M Grad       
Male Und       Fem Grad       
Female Und       Male Und       
        Female Und       
                
         Sum =      
EXPECTED               
M Grad       For this exercise - ignore the requirement for a correction  
Fem Grad       for expected values less than 5.     
Male Und               
Female Und               
                
                
                
                
                
Interpretation:               
    What is the value of the chi square statistic:            
    What is the p-value associated with this value:            
    Is the p-value <0.05?           
    Do you reject or not reject the null hypothesis:            
    If you rejected the null, what is the Cramer's V correlation:           
    What does this correlation mean?           
    What does this decision mean for our equal pay question:            
                
                
4Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern    
 within the population?            
                
 What are the hypothesis statements:           
 Ho:               
 Ha:              
                
          Do manual calculations per cell here (if desired) 
  A BCDEF  A BCDEF
 OBS COUNT - m       M      
 OBS COUNT - f       F      
                
         Sum =       
 EXPECTED              
                
                
                
    What is the value of the chi square statistic:            
    What is the p-value associated with this value:            
    Is the p-value <0.05?           
    Do you reject or not reject the null hypothesis:            
    If you rejected the null, what is the Phi correlation:           
    What does this correlation mean?           
                
    What does this decision mean for our equal pay question:            
                

5.      How do you interpret these results in light of our question about equal pay for equal work?

 

 

Week 5 Correlation and Regression            
                
1.    Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.)    
 a. Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)?   
                
                
 b. Place table here (C8 in Output range box):          
                
 c.Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables are    
  significantly related to Salary?           
  To compa?            
                
 d.Looking at the above correlations - both significant or not - are there any surprises -by that I       
  mean any relationships you expected to be meaningful and are not and vice-versa?       
                
 e.Does this help us answer our equal pay for equal work question?        
                
                
2 Below is a regression analysis for salary being predicted/explained by the other variables in our sample  (Midpoint,     
   age, performance rating, service,  gender, and degree variables. (Note: since salary and compa are different ways of    
   expressing an employee’s salary, we do not want to have both used in the same regression.)      
  Plase interpret the findings.           
                
  Ho: The regression equation is not significant.          
  Ha: The regression equation is significant.          
  Ho: The regression coefficient for each variable is not significant  Note: technically we have one for each input variable.   
  Ha: The regression coefficient for each variable is significant  Listing it this way to save space.     
                
  Sal             
  SUMMARY OUTPUT           
                
  Regression Statistics            
  Multiple R0.9915591            
  R Square0.9831894            
  Adjusted R Square0.9808437            
  Standard Error2.6575926            
  Observations50            
                
  ANOVA             
   dfSSMSFSignificance F        
  Regression617762.32960.38419.15161.812E-36        
  Residual43303.70037.0628          
  Total4918066           
                
   CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%     
  Intercept-1.7496213.618368-0.48350.631166-9.0467555.5475126-9.046755045.54751262     
  Midpoint1.21670110.03190238.13838.66E-351.15236381.28103831.1523638281.28103827     
  Age-0.0046280.065197-0.0710.943739-0.1361110.1268547-0.136110720.1268547     
  Performace Rating-0.0565960.034495-1.64070.108153-0.1261620.0129695-0.126162370.01296949     
  Service-0.04250.084337-0.50390.616879-0.2125820.1275814-0.212582090.12758138     
  Gender2.42033720.8608442.811590.0073970.68427924.15639520.6842791924.15639523     
  Degree0.27553340.7998020.34450.732148-1.3374221.8884885-1.337421651.88848848     
  Note: since Gender and Degree are expressed as 0 and 1, they are considered dummy variables and can be used in a multiple regression equation.  
                
                
  Interpretation:            
  For the Regression as a whole:           
     What is the value of the F statistic:           
     What is the p-value associated with this value:           
     Is the p-value <0.05?          
     Do you reject or not reject the null hypothesis:           
     What does this decision mean for our equal pay question:           
                
  For each of the coefficients: InterceptMidpointAgePerf. Rat.ServiceGenderDegree   
     What is the coefficient's p-value for each of the variables:           
     Is the p-value < 0.05?          
     Do you reject or not reject each null hypothesis:           
     What are the coefficients for the significant variables?          
     Using only the significant variables, what is the equation?Salary =         
     Is gender a significant factor in salary:          
     If so, who gets paid more with all other things being equal?          
     How do we know?           
                
                
3 Perform a regression analysis using compa as the dependent variable and the same independent      
  variables as used in question 2.  Show the result, and interpret your findings by answering the same questions.     
  Note: be sure to include the appropriate hypothesis statements.        
  Regression hypotheses            
  Ho:             
  Ha:             
  Coefficient hypotheses (one to stand for all the separate variables)        
  Ho:             
  Ha:             
  Put C94 in output range box           
                
  Interpretation:            
  For the Regression as a whole:           
     What is the value of the F statistic:           
     What is the p-value associated with this value:           
     Is the p-value < 0.05?          
     Do you reject or not reject the null hypothesis:           
     What does this decision mean for our equal pay question:           
                
  For each of the coefficients:  InterceptMidpointAgePerf. Rat.ServiceGenderDegree   
     What is the coefficient's p-value for each of the variables:           
     Is the p-value < 0.05?          
     Do you reject or not reject each null hypothesis:           
     What are the coefficients for the significant variables?          
     Using only the significant variables, what is the equation?Compa =          
     Is gender a significant factor in compa:          
     If so, who gets paid more with all other things being equal?          
     How do we know?           
                
                
4 Based on all of your results to date, do we have an answer to the question of are males and females paid equally for equal work?   
    If so, which gender gets paid more?            
     How do we know?           
  Which is the best variable to use in analyzing pay practices - salary or compa?  Why?      
  What is most interesting or surprising about the results we got doing the analysis during the last 5 weeks?     
                
                
                
5 Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salary equality question?
  What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test?   
                
       
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