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Complete the problems below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations. All statistical calculations will use the Additional excel attachment Included in the Additional excel attachment Data Set are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. Below are 2 one-sample t-test 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? Based on our sample data set, perform a 2-sample t-test to see if the population male and female average salaries could be equal to each other. (Since we have not yet covered testing for variance equality, assume the data sets have statistically equal variances.) Based on our sample data set, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.) Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders? If the salary and compa mean tests in questions 2 and 3 provide different results about male and female salary equality, which would be more appropriate to use in answering the question about salary equity? Why? What are your conclusions about equal pay at this point?? Complete the problems below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations. All statistical calculations will use the Additional excel attachment Included in the Additional excel attachment Data Set are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. Below are 2 one-sample t-test 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? Based on our sample data set, perform a 2-sample t-test to see if the population male and female average salaries could be equal to each other. (Since we have not yet covered testing for variance equality, assume the data sets have statistically equal variances.) Based on our sample data set, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.) Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders? If the salary and compa mean tests in questions 2 and 3 provide different results about male and female salary equality, which would be more appropriate to use in answering the question about salary equity? Why? What are your conclusions about equal pay at this point?? Complete the problems below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations. All statistical calculations will use the Additional excel attachment Included in the Additional excel attachment Data Set are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. Below are 2 one-sample t-test 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? Based on our sample data set, perform a 2-sample t-test to see if the population male and female average salaries could be equal to each other. (Since we have not yet covered testing for variance equality, assume the data sets have statistically equal variances.) Based on our sample data set, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.) Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders? If the salary and compa mean tests in questions 2 and 3 provide different results about male and female salary equality, which would be more appropriate to use in answering the question about salary equity? Why? What are your conclusions about equal pay at this point?? See comments at the right of the data set. ID Salary Compa Midpoint Age 8 10 11 14 15 23 26 31 35 36 37 42 3 18 20 39 7 13 22 24 45 17 48 28 43 19 25 40 2 32 34 16 27 41 5 30 1 4 12 23 22 23 24 24 23 24 24 24 23 22 24 34 36 34 35 41 42 57 50 55 69 65 75 77 24 24 25 27 28 28 47 40 43 47 49 58 66 60 1.000 0.956 1.000 1.043 1.043 1.000 1.043 1.043 1.043 1.000 0.956 1.043 1.096 1.161 1.096 1.129 1.025 1.050 1.187 1.041 1.145 1.210 1.140 1.119 1.149 1.043 1.043 1.086 0.870 0.903 0.903 1.175 1.000 1.075 0.979 1.020 1.017 1.157 1.052 23 23 23 23 23 23 23 23 23 23 23 23 31 31 31 31 40 40 48 48 48 57 57 67 67 23 23 23 31 31 31 40 40 40 48 48 57 57 57 32 30 41 32 32 36 22 29 23 27 22 32 30 31 44 27 32 30 48 30 36 27 34 44 42 32 41 24 52 25 26 44 35 25 36 45 34 42 52 Performanc Service Gender Raise Degree Gender1 e Rating 90 9 1 5.8 0 F 80 7 1 4.7 0 F 100 19 1 4.8 0 F 90 12 1 6 0 F 80 8 1 4.9 0 F 65 6 1 3.3 1 F 95 2 1 6.2 1 F 60 4 1 3.9 0 F 90 4 1 5.3 1 F 75 3 1 4.3 1 F 95 2 1 6.2 1 F 100 8 1 5.7 0 F 75 5 1 3.6 0 F 80 11 1 5.6 1 F 70 16 1 4.8 1 F 90 6 1 5.5 1 F 100 8 1 5.7 0 F 100 2 1 4.7 1 F 65 6 1 3.8 0 F 75 9 1 3.8 1 F 95 8 1 5.2 0 F 55 3 1 3 0 F 90 11 1 5.3 1 F 95 9 1 4.4 1 F 95 20 1 5.5 1 F 85 1 0 4.6 1 M 70 4 0 4 0 M 90 2 0 6.3 0 M 80 7 0 3.9 0 M 95 4 0 5.6 0 M 80 2 0 4.9 1 M 90 4 0 5.7 0 M 80 7 0 3.9 1 M 80 5 0 4.3 0 M 90 16 0 5.7 1 M 90 18 0 4.3 0 M 85 8 0 5.7 0 M 100 16 0 5.5 1 M 95 22 0 4.5 0 M 33 38 44 46 47 49 50 6 9 21 29 64 56 60 65 62 60 66 76 77 76 72 1.122 0.982 1.052 1.140 1.087 1.052 1.157 1.134 1.149 1.134 1.074 57 57 57 57 57 57 57 67 67 67 67 35 45 45 39 37 41 38 36 49 43 52 90 95 90 75 95 95 80 70 100 95 95 9 11 16 20 5 21 12 12 10 13 5 0 0 0 0 0 0 0 0 0 0 0 5.5 4.5 5.2 3.9 5.5 6.6 4.6 4.5 4 6.3 5.4 1 0 1 1 1 0 0 1 1 1 0 M M M M M M M M M M M Grade A A A A A A A A A A A A B B B B C C D D D E E F F A A A B B B C C C D D E E E The ongoing question that the weekly assignments will focus on is: Are males and females paid the same Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work. The column labels in the table mean: ID – Employee sample number Age – Age in years Service – Years of service (rounded) Midpoint – salary grade midpoint Grade – job/pay grade Gender1 (Male or Female) Salary – Salary in thousands Performance Rating – Appraisal rating (Employee evalua Gender: 0 = male, 1 = female Raise – percent of last raise Degree (0= BS\BA 1 = MS) Compa - salary divided by midpoint E E E E E E E F F F F es and females paid the same for equal work (under the Equal Pay Act)? Week 1. Measurement and Description - chapters 1 and 2 1 Measurement issues. Data, even numerically coded variables, can be one of 4 levels nominal, ordinal, interval, or ratio. It is important to identify which level a variable is, as this impact the kind of analysis we can do with the data. For example, descriptive statistics such as means can only be done on interval or ratio level data. Please list under each label, the variables in our data set that belong in each group. Nominal Ordinal Interval Ratio b. For each variable that you did not call ratio, why did you make that decision? 2 The first step in analyzing data sets is to find some summary descriptive statistics for key variables. For salary, compa, age, performance rating, and service; find the mean, standard deviation, and range for 3 You can use either the Data Analysis Descriptive Statistics tool or the Fx =average and =stdev functions. (the range must be found using the difference between the =max and =min functions with Fx) functions. Note: Place data to the right, if you use Descriptive statistics, place that to the right as well. Salary Compa Age Perf. Rat. Service Overall Mean Standard Deviation Range Female Mean Standard Deviation Range Male Mean Standard Deviation Range 3 What is the probability for a: Probability a. Randomly selected person being a male in grade E? b. Randomly selected male being in grade E? Note part b is the same as given a male, what is probabilty of being in grade E? c. Why are the results different? 4 a. b. c. d. e. f. g. h. i. 5. For each group (overall, females, and males) find: The value that cuts off the top 1/3 salary in each group. The z score for each value: The normal curve probability of exceeding this score: What is the empirical probability of being at or exceeding this salary value? The value that cuts off the top 1/3 compa in each group. The z score for each value: The normal curve probability of exceeding this score: What is the empirical probability of being at or exceeding this compa value? How do you interpret the relationship between the data sets? What do they mean about our equal pay for e What conclusions can you make about the issue of male and female pay equality? Are all of the results co What is the difference between the sal and compa measures of pay? Conclusions from looking at salary results: Conclusions from looking at compa results: Do both salary measures show the same results? Can we make any conclusions about equal pay for equal work yet? Overall Female Male ey mean about our equal pay for equal work question? equality? Are all of the results consistent? Week 2 1 Testing means In questions 2 and 3, be sure to include the null and alternate hypotheses you will be testing. In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the nul Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample me (Note: a one-sample t-test in Excel can be performed by selecting the 2-sample unequal variance t-tes Based on our sample, how do you interpret the results and what do these results suggest about the pop Males Females Ho: Mean salary = 45 Ho: Mean salary = 45 Ha: Mean salary =/= 45 Ha: Mean salary =/= 45 Note: While the results both below are actually from Excel's t-Test: Two-Sample Assuming Unequal having no variance in the Ho variable makes the calculations default to the one-sample t-test outcome Male Ho Mean 52 45 Variance 316 0 Observations 25 25 Hypothesized Mean Difference 0 df 24 t Stat 1.96890383 P(T
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