Expert answer:Week 2 Statistics developing an understanding of t

Solved by verified expert:Week 2—The assignment for this week involves developing an understanding of the problem and the data that we will be analyzing during the class. We will be using a data set of 50 employees sampled from an imaginary company to answer the question of whether males and females receive equal pay for performing equal work.The questions in the assignment follow the examples provided in the weekly guidance lectures.The first question this week focuses on the kind of data we have. Different levels of data allow us to do different kinds of analysis, so we need to understand what we have to work with. Question two involves developing the probability of randomly picking a student who has certain characteristics from the sample. Question three involves finding the probability of randomly picked employees falling within the top one-third of different groups using Excel functions. Question four and five involve using statistical tests to determine if the compa-ratio (an alternate measure of pay).The final question asks for an interpretation of your opinion on the question of equal pay for equal work based on the work done this week. Week 3—During this week, we will look at ways of testing multiple (more than two) data samples at the same time.We will continue to use the data and assignment file that we opened in Week 2, we just move on to the Week 3 tab.The first question asks us to determine if the average compa-ratio is equal across 10K salary groups (20 – 29K. 30 – 39K, etc.). The second question asks us to identify which of the salary groups have different averages. The final question asks us to interpret the new information presented in the lecture and assignment; how does the new information we analyzed help us answer our equal pay for equal work question.Week 4—This week we get to answer our equal pay for equal work question by looking at relationships between and among the different variables.The first question this week looks at correlations and the creation of a correlation table for our variables. The second question asks for a regression equation showing how the different variables impact the compa-ratio measure. The third questions asks you to discuss the benefits of using a regression equation approach over the single variable tests we have been doing.The forth question asks for what other information you would have liked to have analyzed in our research. The fifth question asks for your answer to the equal pay for equal work question of: Is the company paying fairly or not? If not, who benefits and why?
randomized_data.xlsm

student_assignment_file..xlsx

Unformatted Attachment Preview

ID
Salary
Compa
Midpoint
Age
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
61.6
27.7
35.1
58
48.2
78.1
41.3
22.1
73.9
23.1
23.3
64.7
41.1
24
22.6
42.2
63.7
34.5
24.3
34.1
77.2
60.3
23.1
56.3
25
23.5
46.9
78.3
76.3
49.3
23.6
26.5
57.5
28.6
22.6
23.6
23
58.8
33.9
23.8
1.081
57
31
31
57
48
67
40
23
67
23
23
57
40
23
23
40
57
31
23
31
67
48
23
48
23
23
40
67
67
48
23
31
57
31
23
23
23
57
31
23
34
52
30
42
36
36
32
32
49
30
41
52
30
32
32
44
27
31
32
44
43
48
36
30
41
22
35
44
52
45
29
25
35
26
23
27
22
45
27
24
0.895
1.132
1.018
1.004
1.165
1.032
0.962
1.103
1.003
1.012
1.135
1.027
1.045
0.984
1.054
1.118
1.113
1.055
1.101
1.152
1.257
1.004
1.173
1.087
1.020
1.172
1.169
1.139
1.027
1.028
0.855
1.008
0.923
0.984
1.026
0.999
1.032
1.094
1.034
Performance Service Gende Raise
Rating
r
85
80
75
100
90
70
100
90
100
80
100
95
100
90
80
90
55
80
85
70
95
65
65
75
70
95
80
95
95
90
60
95
90
80
90
75
95
95
90
90
8
7
5
16
16
12
8
9
10
7
19
22
2
12
8
4
3
11
1
16
13
6
6
9
4
2
7
9
5
18
4
4
9
2
4
3
2
11
6
2
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
5.7
3.9
3.6
5.5
5.7
4.5
5.7
5.8
4
4.7
4.8
4.5
4.7
6
4.9
5.7
3
5.6
4.6
4.8
6.3
3.8
3.3
3.8
4
6.2
3.9
4.4
5.4
4.3
3.9
5.6
5.5
4.9
5.3
4.3
6.2
4.5
5.5
6.3
41
42
43
44
45
46
47
48
49
50
45.8
24.2
75.6
61.8
56.9
60.2
57.2
69.5
63
59.6
1.144
1.051
1.128
1.085
1.185
1.057
1.003
1.219
1.105
1.046
40
23
67
57
48
57
57
57
57
57
25
32
42
45
36
39
37
34
41
38
80
100
95
90
95
75
95
90
95
80
5
8
20
16
8
20
5
11
21
12
0
1
1
0
1
0
0
1
0
0
4.3
5.7
5.5
5.2
5.2
3.9
5.5
5.3
6.6
4.6
Degree Gender
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
M
M
F
M
M
M
F
F
M
F
F
M
F
F
F
M
F
F
M
F
M
F
F
F
M
F
M
F
M
M
F
M
M
M
F
F
F
M
F
M
Gr
E
B
B
E
D
F
C
A
F
A
A
E
C
A
A
C
E
B
A
B
F
D
A
D
A
A
C
F
F
D
A
B
E
B
A
A
A
E
B
A
The ongoing question that the weekly assignments will focus on is: Are males and fema
Note: to simplfy the analysis, we will assume that jobs within each grade comprise equa
The column labels in the table mean:
ID – Employee sample number
Salary – Salary in thousands
Age – Age in years
Performance Rating – Appraisal rating (em
Service – Years of service (rounded) Gender – 0 = male, 1 = female
Midpoint – salary grade midpoint
Raise – percent of last raise
Grade – job/pay grade
Degree (0= BSBA 1 = MS)
Gender1 (Male or Female)
Compa – salary divided by midpoint
1.06848 0.078873
43.42
19.20121524
1.06132 0.084131
46.8
19.6160436
.
Compa
A
B
C
1.1205
D
F mean
1.014167
1.0375 1.124333
m
1.057333
F Stdev
0.033788
0.031160873 0.017678 0.075162
m
0.024826
0.019052559 0.087797 0.028991
0.892 1.083333
0.9995
0
1
0
1
1
1
1
1
0
0
M
F
F
M
F
M
M
F
M
M
C
A
F
E
D
E
E
E
E
E
will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)?
bs within each grade comprise equal work.
Salary in thousands
ance Rating – Appraisal rating (employee evaluation score)
0 = male, 1 = female
percent of last raise
0= BSBA 1 = MS)
salary divided by midpoint
E
F
1.175
1.134
1.0818
1.12275
0.049497 0.021213
0.060703
0.03326
Sal
Compa
24
1.045
24.2
1.053
23.4
1.018
23.4
1.017
22.6
0.983
22.9
0.995
23.1
1.003
23.3
1.011
22.7
0.985
23.5
1.023
23
1.002
24
1.042
35.5
1.145
34.7
1.119
35.5
1.146
35.2
1.136
40.4
1.01
42.7
1.068
53.4
1.112
51.5
1.072
49.8
1.037
68.3
1.198
65.4
1.148
78.4
1.17
75.9
1.133
24
1.044
23.3
1.012
24.1
1.049
27.5
0.887
27.1
0.875
27.7
0.895
40.8
1.019
43.9
1.097
41
1.025
48.7
1.014
49.4
1.029
64.4
1.13
64.5
1.132
58.9
1.033
57.9
1.016
59
1.035
63.3
1.111
56.8
0.996
G
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Mid
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
57
57
57
57
Age
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
35
45
45
39
EES
90
80
100
90
80
65
95
60
90
75
95
100
75
80
70
90
100
100
65
75
95
55
90
95
95
85
70
90
80
95
80
90
80
80
90
90
85
100
95
90
95
90
75
SR
9
7
19
12
8
6
2
4
4
3
2
8
5
11
16
6
8
2
6
9
8
3
11
9
20
1
4
2
7
4
2
4
7
5
16
18
8
16
22
9
11
16
20
G
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Raise
5.8
4.7
4.8
6
4.9
3.3
6.2
3.9
5.3
4.3
6.2
5.7
3.6
5.6
4.8
5.5
5.7
4.7
3.8
3.8
5.2
3
5.3
4.4
5.5
4.6
4
6.3
3.9
5.6
4.9
5.7
3.9
4.3
5.7
4.3
5.7
5.5
4.5
5.5
4.5
5.2
3.9
Deg
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
58
1.017
62.4
1.094
63.8
1.12
79
1.179
77
1.149
74.8
1.116
76
1.135
0
0
0
0
0
0
0
57
57
57
67
67
67
67
37
41
38
36
49
43
52
95
95
80
70
100
95
95
5
21
12
12
10
13
5
0
0
0
0
0
0
0
5.5
6.6
4.6
4.5
4
6.3
5.4
1
0
0
1
1
1
0
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.705018
R Square
0.49705
Adjusted R Square
0.413225
Standard Error
0.056125
Observations
50
ANOVA
df
Regression
SS
7
MS
42 0.132302
Total
49 0.263052
7.83E-05
0.00315
Coefficients
Standard Error t Stat
0.948624 0.081717 11.60868
Mid
Significance F
0.13075 0.018679 5.929623
Residual
Intercept
F
0.0035 0.000649 5.390013
P-value Lower 95%Upper 95%Lower 95.0%
Upper 95.0%
1.09E-14 0.783713 1.113535 0.783713 1.113535
2.98E-06 0.002189
0.00481 0.002189
0.00481
Age
0.000553 0.001446 0.382293 0.704172
-0.00237 0.003471
-0.00237 0.003471
EES
-0.00185 0.001025
-1.80085 0.078911
-0.00392 0.000223
-0.00392 0.000223
SR
-0.00042 0.001828
-0.22881 0.820124
-0.00411
-0.00411
G
0.064665
Raise
0.014655 0.013909 1.053639 0.298072
-0.01341 0.042724
-0.01341 0.042724
Deg
0.001468
-0.03104 0.033979
-0.03104 0.033979
0.01611
Variable 1 Variable 2
Variance
1.06684
1.04836
0.004302 0.006481
Observations
25
Pooled Variance
0.005391
Hypothesized Mean Difference
0
df
t Stat
48
0.889835
P(T<=t) one-tail 0.188996 t Critical one-tail 1.677224 P(T<=t) two-tail 0.377993 t Critical two-tail 2.010635 0.00327 0.01834 3.525963 0.001035 0.027654 0.101676 0.027654 0.101676 0.0911 0.927847 t-Test: Two-Sample Assuming Equal Variances Mean 0.00327 25 SUMMARY OUTPUT Regression Statistics Multiple R 0.993129 R Square 0.986305 Adjusted R Square 0.984022 Standard Error 2.435282 Observations 50 ANOVA df Regression SS MS F Significance F 7 17938.42 2562.632 432.1034 Residual 42 249.0852 Total 49 18187.51 5.3E-37 5.9306 Coefficients Standard Error t Stat -1.3739 P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% Intercept -4.87145 3.545701 0.17676 -12.027 2.284059 -12.027 2.284059 Mid 1.228416 0.028171 43.60516 Age 0.036828 EES -0.08216 0.044484 SR -0.07785 0.079309 G 2.914508 0.795761 3.662545 0.000694 1.308599 4.520418 1.308599 4.520418 Raise 0.676329 0.603509 1.120662 0.268799 -0.5416 1.894259 -0.5416 1.894259 Deg 0.034504 0.699007 0.049362 0.960865 -1.37615 1.445158 -1.37615 1.445158 1.32E-36 1.171563 1.285268 1.171563 1.285268 0.06274 0.586996 0.560349 -0.08979 0.163442 -0.08979 0.163442 -1.8469 0.071815 -0.17193 0.007615 -0.17193 0.007615 -0.98159 0.331925 -0.2379 0.082203 -0.2379 0.082203 Upper 95.0% ID Salary Compa- Midpoint ratio Age Performance Service Gender Rating Raise Degree Gender 1 Grade Copy Employee Data set to this page. 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 Salary – Salary in thousands Age – Age in years Performance Rating – Appraisal rating (Employee evaluation sco SERvice – Years of service Gender: 0 = male, 1 = female Midpoint – salary grade midpointRaise – percent of last raise Grade – job/pay grade Degree (0= BSBA 1 = MS) Gender1 (Male or Female) Compa-ratio - salary divided by midpoint This assignment covers the material presented in weeks 1 and 2. Six Questions Before starting this assignment, make sure the the assignment data from the Employee Salary Data Set file is copied o You can do this either by a copy and paste of all the columns or by opening the data file, right clicking on the Data ta (Weekly Assignment Sheet or whatever you are calling your master assignment file). It is highly recommended that you copy the data columns (with labels) and paste them to the right so that whatever yo To Ensure full credit for each question, you need to show how you got your results. For example, Question 1 asks fo then the cells should have an "=XX" formula in them, where XX is the column and row number showing the value in value using fx functions, then each function should be located in the cell and the location of the data values should be So, Cell D31 - as an example - shoud contain something like "=T6" or "=average(T2:T26)". Having only a numerica The reason for this is to allow instructors to provide feedback on Excel tools if the answers are not correct - we need In starting the analysis on a research question, we focus on overall descriptive statistics and seeing if differences exis 1 The first step in analyzing data sets is to find some summary descriptive statistics for key variables. Since focus mostly on the compa-ratios, we need to find the mean, standard deviations, and range for our groups Sorting the compa-ratios into male and females will require you copy and paste the Compa-ratio and Gend The values for age, performance rating, and service are provided for you for future use, and - if desired - to (see if you can replicate the values). You can use either the Data Analysis Descriptive Statistics tool or the Fx =average and =stdev functions. The range can be found using the difference between the =max and =min functions with Fx functions or f Suggestion: Copy and paste the compa-ratio data to the right (Column T) and gender data in column U. If you use Descriptive statistics, Place the output table in row 1 of a column to the right. If you did not use Descriptive Statistics, make sure your cells show the location of the da Comparatio Age Perf. Rat. Service Overall Mean 35,7 85,9 9,0 Standard Deviation 8,2513 11,4147 5,7177 Note - remember the da Range 30 45 21 Female Mean 32,5 84,2 7,9 Standard Deviation 6,9 13,6 4,9 Range 26,0 45,0 18,0 Male Mean 38,9 87,6 10,0 Standard Deviation 8,4 8,7 6,4 Range 28,0 30,0 21,0 A key issue in comparing data sets is to see if they are distributed/shaped the same. At this point we can do this by looking at the probabilities that males and females are distributed in the same way for a grade levels. 2 Empirical Probability: What is the probability for a: a. Randomly selected person being in grade E or above? b. Randomly selected person being a male in grade E or above? c. Randomly selected male being in grade E or above? d. Why are the results different? Probability 3 Normal Curve based probability: For each group (overall, females, males), what are the values for each qu Make sure your answer cells show the Excel function and cell location of the data used. The probability of being in the top 1/3 of the compa-ratio distribution. Note, we can find the cutoff value for the top 1/3 using the fx Large function: =large(range, value). Value is the number that identifies the x-largest value. For the top 1/3 value would be the value that starts For the overall group, this would be the 50/3 or 17th (rounded), for the gender groups, it would be the 25/3 A i. ii iii iv. How nany salaries are in the top 1/3 (rounded to nearest whole number) for each group? What Compa-ratio value starts the top 1/3 of the range for each group? What is the z-score for this value? What is the normal curve probability of exceeding this score? B How do you interpret the relationship between the data sets? What does this suggest about our equal pay f 4 A Based on our sample data set, can the male and female compa-ratios in the population be equal to each oth First, we need to determine if these two groups have equal variances, in order to decide which t-test to use. What is the data input ranged used for this question: Step 1: Ho: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell B77 in the output location box. Step 5: Conclusion and Interpretation What is the p-value: Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? What is your decision: REJ or NOT reject the null? What does this result say about our question of variance equality? B Are male and female average compa-ratios equal? (Regardless of the outcome of the above F-test, assume equal variances for this test.) What is the data input ranged used for this question: Step 1: Ho: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell B109 in the output location box. Step 5: Conclusion and Interpretation What is the p-value: Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? What is your decision: REJ or NOT reject the null? What does your decision on rejecting the null hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected? What does the result of this test tell us about our question on salary equality? 5 Is the Female average compa-ratio equal to or less than the midpoint value of 1.00? This question is the same as: Does the company, pay its females - on average - at or below the grade midpo considered the market rate)? Suggestion: Use the data column T to the right for your null hypothesis value. What is the data input ranged used for this question: Step 1: Ho: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell B162 in the output location box. Step 5: Conclusion and Interpretation What is the p-value: Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? What, besides the p-value, needs to be considered with a one tail test? Decision: Reject or do not reject Ho? What does your decision on rejecting the null hypothesis mean? If the null hypothesis was rejected, calculate the effect size value: If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected? What does the result of this test tell us about our question on salary equality? 6 Considering both the salary information in the lectures and your compa-ratio information, what conclusion Why - what statistical results support this conclusion? Probability e the values for each question below?: ge(range, value). d be the value that starts the top 1/3 of the range, ups, it would be the 25/3 = 8th (rounded) value. Overall Female Male est about our equal pay for equal work question? ion be equal to each other? ecide which t-test to use. All of the functions below are in the fx statistical list. Use the "=ROUND" function (found in Math or All list) Use the "=LARGE" function Use Excel's STANDARDIZE function Use "=1-NORM.S.DIST" function or below the grade midpoint (which is Week 3 ANOVA Three Questions Remember to show how you got your results in the appropriate cells. For questions using functions, show the input r 1 One interesting question is are the average compa-ratios equal across salary ranges of 10K each. While compa-ratios remove the impact of grade on salaries, are they different for different pay levels, that is are people at different levels paid differently relative to the midpoint? (Put data values at right.) What is the data input ranged used for this question: Step 1: Ho: Ha: Step 2: Decision Rule: Step 3: Statistical test: Why? Step 4: Conduct the test - place cell b16 in the output location box. Step 5: Conclusions and Interpretation What is the p-value? Is P-value < 0.05? What is your decision: REJ or NOT reject the null? If the null hypothesis was rejected, what is the effect size value (eta squared)? If calculated, what does the effect size value tell us about why the null hypothesis was rejected? What does that decision mean in terms of our equal pay question? 2 If the null hypothesis in question 1 was rejected, which pairs of means differ? Groups Compared G1 G2 G1 G3 G1 G4 G1 G5 G1 G6 Diff T +/- Term Low to G2 G3 G2 G4 G2 G5 G2 G6 G3 G4 G3 G5 G3 G6 G4 G5 G4 G6 G5 G6 3 Since compa is already a measure of pay for equal work, do these results impact your conclusion on equal pay for equal work? Why or why not? High g functions, show the input range when asked. Group name: Salary Intervals: Compa-ratio values: G1 G2 G3 G4 G5 22-29 30-39 40-49 50-59 60-69 Why? Difference Significant? Why? G6 70-79 Regression and Corellation Five Questions Remember to show how you got your results in the appropriate cells. For questions using functions, show the input r 1 Create a correlation table using Compa-ratio and the other interval level variables, except for Sal Suggestion, place data in columns T - Y. What range was placed in the Correlation input range box: Place C9 in output box. b What are the statistically significant correlations related to Compa-ratio? c Are there any surprises - correlations you though would be significant and are not, or non signifi d Why does or does not this information help answer our equal pay question? 2 Perform a regression analysis using compa as the dependent variable and the variables used in Q including the dummy variables. Show the result, and interpret your findings by answering the fo Suggestion: Place the dummy variables values to the right of column Y. What range was placed in the Regression input range box: Note: be sure to include the appropriate hypothesis statements. Regression hypotheses Ho: Ha: Coefficient hyhpotheses (one to stand for all the separate variables) Ho: Ha: Place B36 in output 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? What is your decision: REJ or NOT reject the null? What does this decision mean? For each of the coefficients: 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: Midpoint Age Perf. Rat. What are the coefficients for the significant variables? Using the intercept coefficient and only the significant variables, what is the equation? Compa-ratio = Is gender a significant factor in compa-ratio? Regardless of statistical significance, who gets paid more with all other things being equal? How do we know? 3 What does regression analysis show us about analyzing complex measures? 4 Between the lecture results and your results, what else would you like to know before answering our question on equal pay? Why? 5 Between the lecture results and your results, what is your answer to the question of equal pay for equal work for males and females? Why? functions, show the input range when asked. vel variables, except for Salary. T= Significant r = t and are not, or non significant correlations you thought would be? and the variables used in Q1 along with indings by answering the following questions. Service Gender Degree Compa- Midpoint ratio Age Performa Service nce Raise Degree Gender ... Purchase answer to see full attachment

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