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Statistics Data ID Salary Compa-ratio Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Grade Do not manipuilate Data set on this page, copy to…

Statistics
Data
ID Salary Compa-ratio Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Grade Do not manipuilate Data set on this page, copy to another page to make changes
1 63.2 1.108 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 27.1 0.873 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 35.3 1.138 31 30 75 5 1 3.6 1 F B
4 61.4 1.078 57 42 100 16 0 5.5 1 M E The column labels in the table mean:
5 46.9 0.978 48 36 90 16 0 5.7 1 M D ID – Employee sample number Salary – Salary in thousands
6 74.6 1.113 67 36 70 12 0 4.5 1 M F Age – Age in years Performance Rating – Appraisal rating (employee evaluation score)
7 40.8 1.019 40 32 100 8 1 5.7 1 F C Service – Years of service (rounded) Gender – 0 = male, 1 = female
8 23.8 1.035 23 32 90 9 1 5.8 1 F A Midpoint – salary grade midpoint Raise – percent of last raise
9 74.2 1.108 67 49 100 10 0 4 1 M F Grade – job/pay grade Degree (0= BSBA 1 = MS)
10 23.4 1.017 23 30 80 7 1 4.7 1 F A Gender1 (Male or Female) Compa-ratio – salary divided by midpoint
11 22.3 0.971 23 41 100 19 1 4.8 1 F A
12 64.6 1.134 57 52 95 22 0 4.5 0 M E
13 40.6 1.016 40 30 100 2 1 4.7 0 F C
14 23 0.998 23 32 90 12 1 6 1 F A
15 25.2 1.094 23 32 80 8 1 4.9 1 F A
16 45.7 1.143 40 44 90 4 0 5.7 0 M C
17 70.2 1.231 57 27 55 3 1 3 1 F E
18 34.7 1.119 31 31 80 11 1 5.6 0 F B
19 23.9 1.039 23 32 85 1 0 4.6 1 M A
20 33.5 1.081 31 44 70 16 1 4.8 0 F B
21 71 1.060 67 43 95 13 0 6.3 1 M F
22 52.9 1.103 48 48 65 6 1 3.8 1 F D
23 22.1 0.960 23 36 65 6 1 3.3 0 F A
24 56.8 1.183 48 30 75 9 1 3.8 0 F D
25 24.3 1.056 23 41 70 4 0 4 0 M A
26 24.6 1.071 23 22 95 2 1 6.2 0 F A
27 43.4 1.084 40 35 80 7 0 3.9 1 M C
28 77 1.149 67 44 95 9 1 4.4 0 F F
29 74.7 1.115 67 52 95 5 0 5.4 0 M F
30 47.8 0.995 48 45 90 18 0 4.3 0 M D
31 20.7 0.898 23 29 60 4 1 3.9 1 F A
32 28.6 0.921 31 25 95 4 0 5.6 0 M B
33 59.2 1.038 57 35 90 9 0 5.5 1 M E
34 27.3 0.881 31 26 80 2 0 4.9 1 M B
35 22.9 0.996 23 23 90 4 1 5.3 0 F A
36 22.7 0.987 23 27 75 3 1 4.3 0 F A
37 23.9 1.037 23 22 95 2 1 6.2 0 F A
38 64.7 1.135 57 45 95 11 0 4.5 0 M E
39 35 1.128 31 27 90 6 1 5.5 0 F B
40 23.6 1.024 23 24 90 2 0 6.3 0 M A
41 46.6 1.166 40 25 80 5 0 4.3 0 M C
42 23.3 1.015 23 32 100 8 1 5.7 1 F A
43 76.4 1.140 67 42 95 20 1 5.5 0 F F
44 61.2 1.074 57 45 90 16 0 5.2 1 M E
45 51 1.062 48 36 95 8 1 5.2 1 F D
46 58.8 1.031 57 39 75 20 0 3.9 1 M E
47 66.9 1.174 57 37 95 5 0 5.5 1 M E
48 70.7 1.240 57 34 90 11 1 5.3 1 F E
49 63.5 1.114 57 41 95 21 0 6.6 0 M E
50 64.5 1.132 57 38 80 12 0 4.6 0 M E
Week 1
Week 1: Descriptive Statistics, including Probability
While the lectures will examine our equal pay question from the compa-ratio viewpoint, our weekly assignments will focus on
examining the issue using the salary measure.
The purpose of this assignmnent is two fold:
1. Demonstrate mastery with Excel tools.
2. Develop descriptive statistics to help examine the question.
3. Interpret descriptive outcomes
The first issue in examining salary data to determine if we – as a company – are paying males and females equally for doing equal work is to develop some
descriptive statistics to give us something to make a preliminary decision on whether we have an issue or not.
1 Descriptive Statistics: Develop basic descriptive statistics for Salary
The first step in analyzing data sets is to find some summary descriptive statistics for key variables.
Suggestion: Copy the gender1 and salary columns from the Data tab to columns T and U at the right.
Then use Data Sort (by gender1) to get all the male and female salary values grouped together.
a. Use the Descriptive Statistics function in the Data Analysis tab Place Excel outcome in Cell K19
to develop the descriptive statistics summary for the overall
group’s overall salary. (Place K19 in output range.)
Highlight the mean, sample standard deviation, and range.
b. Using Fx (or formula) functions find the following (be sure to show the formula
and not just the value in each cell) asked for salary statistics for each gender:
Male Female
Mean:
Sample Standard Deviation:
Range:
2 Develop a 5-number summary for the overall, male, and female SALARY variable.
For full credit, show the excel formulas in each cell rather than simply the numerical answer.
Overall Males Females
Max
3rd Q
Midpoint
1st Q
Min
3 Location Measures: comparing Male and Female midpoints to the overall Salary data range.
For full credit, show the excel formulas in each cell rather than simply the numerical answer.
Using the entire Salary range and the M and F midpoints found in Q2 Male Female
a. What would each midpoint’s percentile rank be in the overall range? Use Excel’s =PERCENTRANK.EXC function
b. What is the normal curve z value for each midpoint within overall range? Use Excel’s =STANDARDIZE function
4 Probability Measures: comparing Male and Female midpoints to the overall Salary data range
For full credit, show the excel formulas in each cell rather than simply the numerical answer.
Using the entire Salary range and the M and F midpoints found in Q2, find Male Female
a. The Empirical Probability of equaling or exceeding (=>) that value for Show the calculation formula = value/50 or =countif(range,”>=”&cell)/50
b. The Normal curve Prob of => that value for each group Use “=1-NORM.S.DIST” function
5 Conclusions: What do you make of these results? Be sure to include findings from this week’s lectures as well.
In comparing the overall, male, and female outcomes, what relationship(s) see, to exist between the data sets?
What does this suggest about our equal pay for equal work question?
Week 2
Week 2: Identifying Significant Differences – part 1
To Ensure full credit for each question, you need to show how you got your results. This involves either showing where the data you used is located
or showing the excel formula in each cell. Be sure to copy the appropriate data columns from the data tab to the right for your use this week.
As with our examination of compa-ratio in the lecture, the first question we have about salary between the genders involves equality – are they the same or different?
What we do, depends upon our findings.
1 As with the compa-ratio lecture example, we want to examine salary variation within the groups – are they equal? Use Cell K10 for the Excel test outcome location.
a What is the data input ranged used for this question:
b Which is needed for this question: a one- or two-tail hypothesis statement and test ?
Answer:
Why:
c. Step 1: Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:
Step 5: Conduct the test – place test function in cell k10
Step 6: Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the variance in the population for male and female salaries?
2 Once we know about variance quality, we can move on to means: Are male and female average salaries equal? Use Cell K35 for the Excel test outcome location.
(Regardless of the outcome of the above F-test, assume equal variances for this test.)
a What is the data input ranged used for this question:
b Does this question need a one or two-tail hypothesis statement and test?
Why:
c. Step 1: Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:
Step 5: Conduct the test – place test function in cell K35
Step 6: Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the means in the population for male and female salaries?
3 Education is often a factor in pay differences.
Do employees with an advanced degree (degree = 1) have higher average salaries? Use Cell K60 for the Excel test outcome location.
Note: assume equal variance for the salaries in each degree for this question.
a What is the data input ranged used for this question:
b Does this question need a one or two-tail hypothesis statement and test?
Why:
c. Step 1: Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:
Step 5: Conduct the test – place test function in cell K60
Step 6: Conclusion and Interpretation
What is the p-value:
Is the t value in the t-distribution tail indicated by the arrow in the Ha claim?
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the impact of education on average salaries?
4 Considering both the compa-ratio information from the lectures and your salary information, what conclusions can you reach about equal pay for equal work?
Why – what statistical results support this conclusion?
Week 3
Week 3: Identifying Significant Differences – part 2 Data Input Table: Salary Range Groups
Group name: A B C D E F
To Ensure full credit for each question, you need to show how you got your results. This involves either showing where the data you used is located List salaries within each grade
or showing the excel formula in each cell. Be sure to copy the appropriate data columns from the data tab to the right for your use this week.
1 A good pay program will have different average salaries by grade. Is this the case for our company?
a What is the data input ranged used for this question: Use Cell K08 for the Excel test outcome location.
Note: assume equal variances for each grade, even though this may not be accurate, for purposes of this question.
b. Step 1: Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:
Step 5: Conduct the test – place test function in cell K08
Step 6: Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the means in the population for grade salaries?
2 If the null hypothesis in question 1 was rejected, which pairs of means differ?
(Use the values from the ANOVA table to complete the follow table.)
Groups Compared Mean Diff. T value used +/- Term Low to High Difference Significant? Why?
A-B
A-C
A-D
A-E
A-F
B-C
B-D
B-E
B-E
C-D
C-E
C-F
D-E
D-F
E-F
3 One issue in salary is the grade an employee is in – higher grades have higher salaries.
This suggests that one question to ask is if males and females are distributed in a similar pattern across the salary grades?
a What is the data input ranged used for this question: Use Cell K54 for the Excel test outcome location.
b. Step 1: Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test: Place the actual distribution in the table below.
Why this test? A B C D E F
Step 4: Decision rule: Male
Step 5: Conduct the test – place test function in cell K54 Female
Step 6: Conclusion and Interpretation Place the expected distribution in the table below.
What is the p-value: A B C D E F
What is your decision: REJ or NOT reject the null? Male
Why? Female
What is your conclusion about the means in the population for male and female salaries?
4 What implications do this week’s analysis have for our equal pay question?
Why – what statistical results support this conclusion?
Week 4
Week 4: Identifying relationships – correlations and regression
To Ensure full credit for each question, you need to show how you got your results. This involves either showing where the data you used is located
or showing the excel formula in each cell. Be sure to copy the appropriate data columns from the data tab to the right for your use this week.
1 What is the correlation between and among the interval/ratio level variables with salary? (Do not include compa-ratio in this question.)
a. Create the correlation table. Use Cell K08 for the Excel test outcome location.
i. What is the data input ranged used for this question:
ii. Create a correlation table in cell K08.
b. Technically, we should perform a hypothesis testing on each correlation to determine
if it is significant or not. However, we can be faithful to the process and save some
time by finding the minimum correlation that would result in a two tail rejection of the null.
We can then compare each correlation to this value, and those exceeding it (in either a
positive or negative direction) can be considered statistically significant.
i. What is the t-value we would use to cut off the two tails? T =
ii. What is the associated correlation value related to this t-value? r =
c. What variable(s) is(are) significantly correlated to salary?
d. Are there any surprises – correlations you though would be significant and are not, or non significant correlations you thought would be?
e. Why does or does not this information help answer our equal pay question?
2 Perform a regression analysis using salary as the dependent variable and the variables used in Q1 along with
our two dummy variables – gender and education. Show the result, and interpret your findings by answering the following questions.
Suggestion: Add the dummy variables values to the right of the last data columns used for Q1.
What is the multiple regression equation predicting/explaining salary using all of our possible variables except compa-ratio?
a. What is the data input ranged used for this question:
b. Step 1: State the appropriate hypothesis statements: Use Cell M34 for the Excel test outcome location.
Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:
Step 5: Conduct the test – place test function in cell M34
Step 6: Conclusion and Interpretation
What is the p-value:
What is your decision: REJ or NOT reject the null?
Why?
What is your conclusion about the factors influencing the population compa-ratio values?
c. If we rejected the null hypothesis, we need to test the significance of each of the variable coefficients.
Step 1: State the appropriate coefficient hypothesis statements: (Write a single pair, we will use it for each variable separately.)
Ho:
Ha:
Step 2: Significance (Alpha):
Step 3: Test Statistic and test:
Why this test?
Step 4: Decision rule:
Step 5: Conduct the test
Note, in this case the test has been performed and is part of the Regression output above.
Step 6: Conclusion and Interpretation
Place the t and p-values in the following table
Identify your decision on rejecting the null for each variable. If you reject the null, place the coefficient in the table.
Midpoint Age Perf. Rat. Seniority Raise Gender Degree
t-value:
P-value:
Rejection Decision:
If Null is rejected, what is the variable’s coefficient value?
Using the intercept coefficient and only the significant variables, what is the equation?
Salary =
d. Is gender a significant factor in compa-ratio?
e. Regardless of statistical significance, who gets paid more with all other things being equal?
f. How do we know?
3 After considering the compa-ratio based results in the lectures and your saalary based results, what else would you like to know
before answering our question on equal pay? Why?
4 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?
5 What does regression analysis show us about analyzing complex measures?

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