Raw Preview of Attachment:(refer to the detailed question and attachment below)
IDSalCompaMidAgeEESSRGRaiseDegGen1GrMEBFDCASal – Salary in thousands Age – Age in yearsEES – Appraisal rating (Employee evaluation score)SER – Years of serviceMid – salary grade midpoint Raise – percent of last raiseGrade – job/pay gradeDeg (0= BS\BA 1 = MS)Gen1 (Male or Female)The column labels in the table mean:sal, compa, age, sr and raise.Week 1.Week 2Week 4Week 3Week 5 Correlation and Regression G – Gender (0 = male, 1 = female) ID – Employee sample number Describing the data.The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.GradeGenderQ1Q2which would be more appropriate to use in answering the question about salary equity? Why? expressing an employee’s salary, we do not want to have both used in the same regression.)Set up the input table/range to use as follows: Put all of the salary values for each grade under the appropriate grade label.a. For which variables in the data set does this function not work correctly for? Why?c. Why are the results different?Use either the descriptive stats function or the Fx functions (average and stdev).For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed.Testing multiple means with ANOVATesting means with the t-testFor each question involving a statistical test below, list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions.Hint: use mean values in the boxes.Are all of the results consistent with your conclusion? If not, why not?Ho: Mean salary = 45Ha: Mean salary =/= 45Perform analysis:t-Test: Two-Sample Assuming Unequal VariancesSince the Ho variable has Var = 0, variances are unequal; this test defaults to 1 sample t in this situationMaleHoFemaleMeanVarianceObservationsHypothesized Mean Differencedft StatP(T<=t) one-tailt Critical one-tailP(T<=t) two-tailt Critical two-tailConclusion: Do not reject Ho; mean equals 45MalesFemalesInterpretation:Based on our sample results, perform a 2-sample t-test to see if the population male and female salaries could be equal to each other.Based on our sample results, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.)Note when performing a one sample test with ANOVA, the second variable (Ho) is listed as the same value for every corresponding value in the data set.Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. If the salary and compa mean tests in questions 3 and 4 provide different results about male and female salary equality, Compa - salary divided by midpoint, a measure of salary that removes the impact of gradeWhy might we want to use compa to measure salaries between males and females?<Use right click on the row numbers at the left to insert rows below each question for your results and comments.>What other information would you like to know to answer the question about salary equity between the genders? Why?The salary values were randomly picked for each cell.Ho: Average salaries are equal for all gradesHa: Average salaries are not equal for all gradesHo: Average salaries by gender are equalHa: Average salaries by gender are not equalHo: Interaction is not significantHa: Interaction is significantAnova: Two-Factor With ReplicationSUMMARYTotalCountSumAverageANOVASource of VariationSSMSP-valueF critSampleColumnsInteractionWithinUsing our sample results, can we say that the compa values in the population are equal by grade and/or gender, and are independent of each factor?<Randomly pick compas to fill each cell - for exampe, a compafor the intersection of M and A might be 1.043.>Interpret the results. Are the average compas for each gender (listed as sample) equal? For each grade? Do grade and gender interaction impact compa values? Using the results for this week, What are your conclusions about gender equal pay for equal work at this point?<If desired, you can use the compa values that relate to the salary values used in question 2 for a more direct comparison of the two outcomes.>Conduct and show the results of a 2-way ANOVA with replication using the completed table above. The results should look something like those in question 2.Variable name: 1. Based on the sample data, can the average(mean) salary in the population be the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.) Pick any other variable you are interested in and do a simple 2-way ANOVA without replication. Why did you pick this variable and what do the results show?A EXPECTED<Highlighting each cell with show how the valueis found: row total times column total divided bygrand total.>Ho: The populaton correlation between grade and degree is 0.Ha: The population correlation between grade and degree is > 0By using either the Excel Chi Square functions or calculating the results directly as the text shows, do wereject or not reject the null hypothesis? What does your conclusion mean?Do we reject or not reject each of the null hypotheses? What do your conclusions mean about the population values being tested?2. Interpret the results. How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)?Low to HighSt error <Reminder: standard error is the sample standard deviation divided by the square root of the sample size.>Do they intersect or overlap? How do these results compare to the findings in week 2, question 2?Results are mean +/-2.064*standard error2.064 is t value for 95% intervalHow do you interpret these results in light of our question about equal pay for equal work?Create a correlation table for the variables in our data set. (Use analysis ToolPak function Correlation.)Based on all of your results to date, is gender a factor in the pay practices of this company? Why or why not?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?SUMMARY OUTPUTRegression StatisticsMultiple RR SquareAdjusted R SquareStandard ErrorSignificance FRegressionResidualCoefficientsLower 95%Upper 95%Lower 95.0%Upper 95.0%InterceptThe analysis used Sal as the y (dependent variable) andvariables (entered as a range).Ho: The regression equation is not significant.Ha: The regression coefficient for each variable is significantHo: The regression coefficient for each variable is not significant Do you reject or not reject the regression null hypothesis?Do you reject or not reject the null hypothesis for each variable?What is the regression equation, using only significant variables if any exist?What does result tell us about equal pay for equal work for males and females?Which is the best variable to use in analyzing pay practices - salary or compa? Why?Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Mid,Note: a number with an E after it (E9 or E-6, for example)means we move the decimal point that number of places.For example, 1.2E4 becomes 12000; while 4.56E-5 becomes 0.0000456(Note: this is the same as asking if the degrees are distributed the same way.)totalOBSERVEDCOUNT - M or 0 COUNT - F or 1For 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. Let's look at some other factors that might influence pay.3. 4. 5. <Note: use right click on row numbers to insert rows to perform analysis below any question>For questions 2 and 3 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions.Based on this sample, what conclusions can you make about the issue of male and female pay equality? Find:What is the probability for a: Sort the data by Gen or Gen 1 (into males and females) and find the mean and standard deviation for each gender for the following variables:Using the Excel Analysis ToolPak function descriptive statistics, generate and show the descriptive statistics for each appropriate variable in the sample data set.The analysis tool pak has been removed from Excel for Windows, but a free third-party tool that can be used (found on an answers Microsoft site) is:http://www.analystsoft.com/en/products/statplusmacleLike the Microsoft site, I make cannot guarantee the program, but do know that Statplus is a respected statistical package.Mac Users: The homework in this course assumes students have Windows Excel, andcan load the Analysis ToolPak into their version of Excel.This data should be treated as a sample of employees taken from a company that has about 1,000 employees using a random sampling approach.You may use other approaches or toolsas desired to complete the assignments.a. Randomly selected person being a male in grade E?b. Randomly selected male being in grade E?a.b.c.d.e. The z score for each male salary, based on only the male salaries.The z score for each female salary, based on only the female salaries.The z score for each male compa, based on only the male compa values.What do the distributions and spread suggest about male and female salaries?The z score for each female compa, based on only the female compa values.Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female salaries?What are your conclusions about equal pay at this point?Be sure to incllude the null and alternate hypothesis along with the statistical test and result.Note: Assume equal variances for all grades.Confidence Intervals and Chi Square (Chs 11 - 12)One question we might have is if the distribution of graduate and undergraduate degrees independent of the grade the employee? Based on the analysis of our sample data (shown below), what is your answer?Using our sample data, we can construct a 95% confidence interval for the population's mean salary for each gender. For question 3 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions.a. Interpret the results. What variables seem to be important in seeing if we pay males and females equally for equal work?The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results. age, ees, sr, raise, and deg variables.) (Note: since salary and compa are different ways ofWhat outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test?Perform a regression analysis using compa as the dependent variable and the same independentvariables 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.Ha: The regression equation is significant.mid, age, ees, sr, g, raise, and deg as the dependent Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population? Be sure to include the null and alternate hypothesis along with the statistical test and result.SERUsing our sample data, construct a 95% confidence interval for the population's mean service difference for each gender.
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