I'm having a hard time with week 3. We are using data from week 1. Attachment Preview: ID Sal Compa Mid Age EES SER G Raise Deg Gen1 Gr 1 58 1.017 57 34 85 8 0 5.7 0 M E 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)? 2 27 0.870 31 52 80 7 0 3.9 0 M B Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work. 3 34 1.096 31 30 75 5 1 3.6 1 F B 4 66 1.157 57 42 100 16 0 5.5 1 M E The column labels in the table mean: 5 47 0.979 48 36 90 16 0 5.7 1 M D ID – Employee sample number Sal – Salary in thousands 6 76 1.134 67 36 70 12 0 4.5 1 M F Age – Age in years EES – Appraisal rating (Employee evaluation score) 7 41 1.025 40 32 100 8 1 5.7 1 F C SER – Years of service G – Gender (0 = male, 1 = female) 8 23 1.000 23 32 90 9 1 5.8 1 F A Mid – salary grade midpoint Raise – percent of last raise 9 77 1.149 67 49 100 10 0 4 1 M F Grade – job/pay grade Deg (0= BS\BA 1 = MS) 10 22 0.956 23 30 80 7 1 4.7 1 F A Gen1 (Male or Female) Compa - salary divided by midpoint, a measure of salary that removes the impact of grade 11 23 1.000 23 41 100 19 1 4.8 1 F A 12 60 1.052 57 52 95 22 0 4.5 0 M E This data should be treated as a sample of employees taken from a company that has about 1,000 13 42 1.050 40 30 100 2 1 4.7 0 F C employees using a random sampling approach. 14 24 1.043 23 32 90 12 1 6 1 F A 15 24 1.043 23 32 80 8 1 4.9 1 F A 16 47 1.175 40 44 90 4 0 5.7 0 M C Mac Users: The homework in this course assumes students have Windows Excel, and 17 69 1.210 57 27 55 3 1 3 1 F E can load the Analysis ToolPak into their version of Excel. 18 36 1.161 31 31 80 11 1 5.6 0 F B The analysis tool pak has been removed from Excel for Windows, but a free third-party 19 24 1.043 23 32 85 1 0 4.6 1 M A tool that can be used (found on an answers Microsoft site) is: 20 34 1.096 31 44 70 16 1 4.8 0 F B http://www.analystsoft.com/en/products/statplusmacle 21 76 1.134 67 43 95 13 0 6.3 1 M F Like the Microsoft site, I make cannot guarantee the program, but do know that 22 57 1.187 48 48 65 6 1 3.8 1 F D Statplus is a respected statistical package. You may use other approaches or tools 23 23 1.000 23 36 65 6 1 3.3 0 F A as desired to complete the assignments. 24 50 1.041 48 30 75 9 1 3.8 0 F D 25 24 1.043 23 41 70 4 0 4 0 M A 26 24 1.043 23 22 95 2 1 6.2 0 F A 27 40 1.000 40 35 80 7 0 3.9 1 M C 28 75 1.119 67 44 95 9 1 4.4 0 F F 29 72 1.074 67 52 95 5 0 5.4 0 M F 30 49 1.020 48 45 90 18 0 4.3 0 M D 31 24 1.043 23 29 60 4 1 3.9 1 F A 32 28 0.903 31 25 95 4 0 5.6 0 M B 33 64 1.122 57 35 90 9 0 5.5 1 M E 34 28 0.903 31 26 80 2 0 4.9 1 M B 35 24 1.043 23 23 90 4 1 5.3 0 F A 36 23 1.000 23 27 75 3 1 4.3 0 F A 37 22 0.956 23 22 95 2 1 6.2 0 F A 38 56 0.982 57 45 95 11 0 4.5 0 M E 39 35 1.129 31 27 90 6 1 5.5 0 F B 40 25 1.086 23 24 90 2 0 6.3 0 M A 41 43 1.075 40 25 80 5 0 4.3 0 M C 42 24 1.043 23 32 100 8 1 5.7 1 F A 43 77 1.149 67 42 95 20 1 5.5 0 F F 44 60 1.052 57 45 90 16 0 5.2 1 M E 45 55 1.145 48 36 95 8 1 5.2 1 F D 46 65 1.140 57 39 75 20 0 3.9 1 M E 47 62 1.087 57 37 95 5 0 5.5 1 M E 48 65 1.140 57 34 90 11 1 5.3 1 F E 49 60 1.052 57 41 95 21 0 6.6 0 M E 50 66 1.157 57 38 80 12 0 4.6 0 M E Week 1. Describing the data.

1 Using the Excel Analysis ToolPak function descriptive statistics, generate and show the descriptive statistics for each appropriate variable in the sample data set. a. For which variables in the data set does this function not work correctly for? Why? 2 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: sal, compa, age, sr and raise. Use either the descriptive stats function or the Fx functions (average and stdev). 3 What is the probability for a: a. Randomly selected person being a male in grade E? b. Randomly selected male being in grade E? c. Why are the results different? 4 Find: a. The z score for each male salary, based on only the male salaries. b. The z score for each female salary, based on only the female salaries. c. The z score for each female compa, based on only the female compa values. d. The z score for each male compa, based on only the male compa values. e. What do the distributions and spread suggest about male and female salaries? Why might we want to use compa to measure salaries between males and females? 5 Based on this sample, what conclusions can you make about the issue of male and female pay equality? Are all of the results consistent with your conclusion? If not, why not? Week 2 Testing means with the t-test 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. For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed. 1 Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. 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? Males Females Ho: Mean salary = 45 Ho: Mean salary = 45 Ha: Mean salary =/= 45 Ha: Mean salary =/= 45 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. t-Test: Two-Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances Since the Ho variable has Var = 0, variances are unequal; this test defaults to 1 sample t in this situation Male Ho Female Ho Mean 52 45 Mean 38 45 Variance 316 0 Variance 334.6666667 0 Observations 25 25 Observations 25 25 Hypothesized Mean Difference 0 Hypothesized Mean Difference 0 df 24 df 24 t Stat 1.968903827 t Stat -1.913206357 P(T<=t) > 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. 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.) Set up the input table/range to use as follows: Put all of the salary values for each grade under the appropriate grade label. Be sure to incllude the null and alternate hypothesis along with the statistical test and result. A B C D E F Note: Assume equal variances for all grades. 2. The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results. Grade Gender A B C D E F M 24 27 40 47 56 76 The salary values were randomly picked for each cell. 25 28 47 49 66 77 F 22 34 41 50 65 75 24 36 42 57 69 77 Ho: Average salaries are equal for all grades Ha: Average salaries are not equal for all grades Ho: Average salaries by gender are equal Ha: Average salaries by gender are not equal Ho: Interaction is not significant Ha: Interaction is significant Perform analysis: Anova: Two-Factor With Replication SUMMARY A B C D E F Total M Count 2 2 2 2 2 2 12 Sum 49 55 87 96 122 153 562 Average 24.5 27.5 43.5 48 61 76.5 46.83333333 Variance 0.5 0.5 24.5 2 50 0.5 364.5151515 F Count 2 2 2 2 2 2 12 Sum 46 70 83 107 134 152 592 Average 23 35 41.5 53.5 67 76 49.33333333 Variance 2 2 0.5 24.5 8 2 367.3333333 Total Count 4 4 4 4 4 4 Sum 95 125 170 203 256 305 Average 23.75 31.25 42.5 50.75 64 76.25 Variance 1.583333333 19.58333333 9.666666667 18.91666667 31.33333333 0.916666667 ANOVA Source of Variation SS df MS F P-value F crit Sample 37.5 1 37.5 3.846153846 0.073483337 4.747225347 Columns 7841.833333 5 1568.366667 160.8581197 1.45206E-10 3.105875239 Note: a number with an E after it (E9 or E-6, for example) Interaction 91.5 5 18.3 1.876923077 0.172308261 3.105875239 means we move the decimal point that number of places. Within 117 12 9.75 For example, 1.2E4 becomes 12000; while 4.56E-5 becomes 0.0000456 Total 8087.833333 23 Do we reject or not reject each of the null hypotheses? What do your conclusions mean about the population values being tested? Interpretation: 3. Using 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? Grade Be sure to include the null and alternate hypothesis along with the statistical test and result. Gender A B C D E F 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. 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? 4. 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? Variable name: Be sure to include the null and alternate hypothesis along with the statistical test and result. Gender A B C D E F M Hint: use mean values in the boxes. F 5. Using the results for this week, What are your conclusions about gender equal pay for equal work at this point?