week three problem set

profileantmidd026
09CanvasBUS308SEP2018StudentWorksheetnew_Progress1newweek23.xlsx
Home>Mathematics homework help>Statistics homework help>week three problem set

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 54.5 0.956 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 28.3 0.913 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 1.100 31 30 75 5 1 3.6 1 F B
4 60.9 1.068 57 42 100 16 0 5.5 1 M E The column labels in the table mean:
5 49.2 1.025 48 36 90 16 0 5.7 1 M D ID – Employee sample number Salary – Salary in thousands
6 74.1 1.106 67 36 70 12 0 4.5 1 M F Age – Age in years Performance Rating - Appraisal rating (employee evaluation score)
7 41.4 1.034 40 32 100 8 1 5.7 1 F C Service – Years of service (rounded) Gender – 0 = male, 1 = female
8 22.8 0.992 23 32 90 9 1 5.8 1 F A Midpoint – salary grade midpoint Raise – percent of last raise
9 73 1.089 67 49 100 10 0 4 1 M F Grade – job/pay grade Degree (0= BS\BA 1 = MS)
10 23.3 1.014 23 30 80 7 1 4.7 1 F A Gender1 (Male or Female) Compa-ratio - salary divided by midpoint
11 24.3 1.057 23 41 100 19 1 4.8 1 F A
12 59.7 1.047 57 52 95 22 0 4.5 0 M E
13 41.8 1.044 40 30 100 2 1 4.7 0 F C
14 25 1.085 23 32 90 12 1 6 1 F A
15 22.6 0.983 23 32 80 8 1 4.9 1 F A
16 48.5 1.213 40 44 90 4 0 5.7 0 M C
17 63.1 1.107 57 27 55 3 1 3 1 F E
18 36.2 1.167 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 35.5 1.144 31 44 70 16 1 4.8 0 F B
21 78.9 1.178 67 43 95 13 0 6.3 1 M F
22 57.6 1.199 48 48 65 6 1 3.8 1 F D
23 22.2 0.964 23 36 65 6 1 3.3 0 F A
24 53.4 1.112 48 30 75 9 1 3.8 0 F D
25 23.6 1.028 23 41 70 4 0 4 0 M A
26 22.3 0.971 23 22 95 2 1 6.2 0 F A
27 46.2 1.156 40 35 80 7 0 3.9 1 M C
28 74.4 1.111 67 44 95 9 1 4.4 0 F F
29 75.6 1.129 67 52 95 5 0 5.4 0 M F
30 47.5 0.989 48 45 90 18 0 4.3 0 M D
31 22.9 0.995 23 29 60 4 1 3.9 1 F A
32 28.1 0.906 31 25 95 4 0 5.6 0 M B
33 63.7 1.117 57 35 90 9 0 5.5 1 M E
34 26.9 0.869 31 26 80 2 0 4.9 1 M B
35 22.7 0.987 23 23 90 4 1 5.3 0 F A
36 24.4 1.059 23 27 75 3 1 4.3 0 F A
37 23.8 1.034 23 22 95 2 1 6.2 0 F A
38 64.6 1.133 57 45 95 11 0 4.5 0 M E
39 37.3 1.202 31 27 90 6 1 5.5 0 F B
40 23.7 1.031 23 24 90 2 0 6.3 0 M A
41 40.3 1.008 40 25 80 5 0 4.3 0 M C
42 24.4 1.059 23 32 100 8 1 5.7 1 F A
43 72.3 1.079 67 42 95 20 1 5.5 0 F F
44 65.9 1.156 57 45 90 16 0 5.2 1 M E
45 49.9 1.040 48 36 95 8 1 5.2 1 F D
46 57.4 1.007 57 39 75 20 0 3.9 1 M E
47 56 0.982 57 37 95 5 0 5.5 1 M E
48 68.1 1.195 57 34 90 11 1 5.3 1 F E
49 66.2 1.161 57 41 95 21 0 6.6 0 M E
50 61.7 1.083 57 38 80 12 0 4.6 0 M E

Week 1

Week 1: Descriptive Statistics, including Probability Gender1 Salary
While the lectures will examine our equal pay question from the compa-ratio viewpoint, our weekly assignments will focus on F 34.1
examining the issue using the salary measure. F 41.4
F 22.8
The purpose of this assignmnent is two fold: F 23.3
1. Demonstrate mastery with Excel tools. F 24.3
2. Develop descriptive statistics to help examine the question. F 41.8
3. Interpret descriptive outcomes F 25
F 22.6
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 F 63.1
descriptive statistics to give us something to make a preliminary decision on whether we have an issue or not. F 36.2
F 35.5
1 Descriptive Statistics: Develop basic descriptive statistics for Salary F 57.6
The first step in analyzing data sets is to find some summary descriptive statistics for key variables. F 22.2
Suggestion: Copy the gender1 and salary columns from the Data tab to columns T and U at the right. F 53.4
Then use Data Sort (by gender1) to get all the male and female salary values grouped together. F 22.3
F 74.4
a. Use the Descriptive Statistics function in the Data Analysis tab Place Excel outcome in Cell K19 F 22.9
to develop the descriptive statistics summary for the overall Column1 F 22.7
group's overall salary. (Place K19 in output range.) F 24.4
Highlight the mean, sample standard deviation, and range. Mean 44.884 F 23.8
Standard Error 2.6698167177 F 37.3
Median 44 F 24.4
Mode 24.4 F 72.3
b. Using Fx (or formula) functions find the following (be sure to show the formula 18.8784550561 Standard Deviation 18.8784550561 F 49.9
and not just the value in each cell) asked for salary statistics for each gender: Sample Variance 356.3960653061 F 68.1
Male Female Kurtosis -1.4241756975 M 54.5
Mean: 51.936 37.832 Skewness 0.2096662654 M 28.3
Sample Standard Deviation: 17.7426247588 17.5850959622 Range 56.7 M 60.9
Range: 55.3 52.2 Minimum 22.2 M 49.2
Maximum 78.9 M 74.1
Sum 2244.2 M 73
Count 50 M 59.7
M 48.5
2 Develop a 5-number summary for the overall, male, and female SALARY variable. M 23.9
For full credit, use the excel formulas in each cell rather than simply the numerical answer. M 78.9
Overall Males Females M 23.6
Max 78.9 78.9 74.4 M 46.2
3rd Q 61.5 64.6 49.9 M 75.6
Midpoint 44 56 34.1 M 47.5
1st Q 24.4 40.3 23.3 M 28.1
Min 44.4 23.6 22.2 0 M 63.7
0.37 M 26.9
3 Location Measures: comparing Male and Female midpoints to the overall Salary data range. M 64.6
For full credit, show the excel formulas in each cell rather than simply the numerical answer. M 23.7
Using the entire Salary range and the M and F midpoints found in Q2 Male Female M 40.3
a. What would each midpoint's percentile rank be in the overall range? 0.64 0.37 Use Excel's =PERCENTRANK.EXC function M 65.9
b. What is the normal curve z value for each midpoint within overall range? 0.5888 -0.5712 Use Excel's =STANDARDIZE function M 57.4
M 56
4 Probability Measures: comparing Male and Female midpoints to the overall Salary data range 0.64 M 66.2
For full credit, show the excel formulas in each cell rather than simply the numerical answer. M 61.7
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 0.36 0.64 Show the calculation formula = value/50 or =countif(range,">="&cell)/50
b. The Normal curve Prob of => that value for each group 0.3594235668 0.2610862997 Use "=1-NORM.S.DIST" function
Note: be sure to use the ENTIRE salary range for part a when finding the probability.
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?
Your findings: it is my finding that half the males make more than the females and the other half of the males make less than the females. Of the 56 compared to the statistical prediction
The lecture's related findings: the lecture makes that argument that all the males make a larger salary but that is not the case.
Overall conclusion: is after you range and midpoint to figure out the number of people that make larger salary and how many make less than female in the company
What does this suggest about our equal pay for equal work question?

Week 2

Week 2: Identifying Significant Differences - part 1 Salary Compa-ratio
Male Femael Male Female
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 54.5 34.1 0.956 1.100
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. 28.3 41.4 0.913 1.034
60.9 22.8 1.068 0.992
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? 49.2 23.3 1.025 1.014
What we do, depends upon our findings. 74.1 24.3 1.106 1.057
73 41.8 1.089 1.044
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. 59.7 25 1.047 1.085
a What is the data input ranged used for this question: F-Test Two-Sample for Variances 48.5 22.6 1.213 0.983
Q3:Q27 and R3:R27 23.9 63.1 1.039 1.107
b Which is needed for this question: a one- or two-tail hypothesis statement and test ? Male Female 78.9 36.2 1.178 1.167
Answer: I would pick the one tail hypothesis Mean 1.05556 1.06936 23.6 35.5 1.028 1.144
Why: We are only trying to prove that they are not equal Variance 0.0081384233 0.0052293233 46.2 57.6 1.156 1.199
Observations 25 25 75.6 22.2 1.129 0.964
c. Step 1: Ho: Male compa-ratio variance equl Female compa-ratio variance df 24 24 47.5 53.4 0.989 1.112
Ha: Male compa-ratio variance not equl Female compa-ratio variance F 1.5563052454 28.1 22.3 0.906 0.971
Step 2: Significance (Alpha): 0.05 P(F<=f) one-tail 0.1427728797 63.7 74.4 1.117 1.111
Step 3: Test Statistic and test: F statistic and F-test for Variance F Critical one-tail 1.9837595685 26.9 22.9 0.869 0.995
Why this test? Need to determine the mean and significantly different 64.6 22.7 1.133 0.987
Step 4: Decision rule: Decision rule: Reject the null hypothesis if the p-value is less than 0.05 23.7 24.4 1.031 1.059
Step 5: Conduct the test - place test function in cell k10 40.3 23.8 1.008 1.034
65.9 37.3 1.156 1.202
Step 6: Conclusion and Interpretation 57.4 24.4 1.007 1.059
What is the p-value: 0.1427728797 56 72.3 0.982 1.079
What is your decision: REJ or NOT reject the null? Not Reject 66.2 49.9 1.161 1.040
Why? p value is greater than alpha 61.7 68.1 1.083 1.195
What is your conclusion about the variance in the population for male and female salaries? Conclude that Male compa-ratio variance equl Female compa-ratio variance
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: F-Test Two-Sample for Variances
03:027 and P3:P27
b Does this question need a one or two-tail hypothesis statement and test? two tail hypothesis Male Femael
Why: We trying to prove that they are not equal Mean 51.936 37.832
c. Step 1: Ho: male salary average=female salary average Variance 314.8007333333 309.2356
Ha: male salary average=/female salary average Observations 25 25
Step 2: Significance (Alpha): 0.05 df 24 24
Step 3: Test Statistic and test: F-test F 1.0179964187
Why this test? because we are dealing with two tail P(F<=f) one-tail 0.4827562326
Step 4: Decision rule: Reject the null hypothesis if the p-value is less than our alpha of .05 F Critical one-tail 1.9837595685
Step 5: Conduct the test - place test function in cell K35 P(F<=f) 2-tail 0.9655124652
Step 6: Conclusion and Interpretation
What is the p-value: 0.9655124652
What is your decision: REJ or NOT reject the null? Not Reject
Why? p value is greater than alpha (0.05)
What is your conclusion about the means in the population for male and female salaries?
Cocnclude that male salary average is equal female salary average
The means did not equal at all . The males had a higher variance as well
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. Degree
Note: assume equal variance for the salaries in each degree for this question. 0 1
a What is the data input ranged used for this question: t-Test: Paired Two Sample for Means Salary 0 Salary 1
N59:N83 and O59:O83 54.5 34.1
b Does this question need a one or two-tail hypothesis statement and test? one tail Salary 0 Salary1 28.3 60.9
Why: We are only looking at who has a degree or not Mean 43.544 46.224 59.7 49.2
c. Step 1: Ho: degree have equal average salaries Variance 339.2742333333 384.6269 41.8 74.1
Ha: degree have higher average salaries Observations 25 25 48.5 41.4
Step 2: Significance (Alpha): 0.05 Pearson Correlation 0.1040068904 36.2 22.8
Step 3: Test Statistic and test: t-Test: Paired Two Sample for Means Hypothesized Mean Difference 0 35.5 73
Why this test? because of the infomration in use df 24 22.2 23.3
Step 4: Decision rule: Reject the null hypothesis if the p-value is less than our alpha of .05 t Stat -0.5260939696 53.4 24.3
Step 5: Conduct the test - place test function in cell K60 P(T<=t) one-tail 0.3018255069 23.6 25
t Critical one-tail 1.7108820799 22.3 22.6
Step 6: Conclusion and Interpretation P(T<=t) two-tail 0.6036510137 74.4 63.1
What is the p-value: 0.6036510137 t Critical two-tail 2.0638985616 75.6 23.9
Is the t value in the t-distribution tail indicated by the arrow in the Ha claim? Yes 47.5 78.9
28.1 57.6
What is your decision: REJ or NOT reject the null? Not Reject 22.7 46.2
Why? P value is greater than 0.05 24.4 22.9
What is your conclusion about the impact of education on average salaries? 23.8 63.7
conclude that degree have equal average salaries 64.6 26.9
37.3 24.4
it was shown that education had a good impart on salary with the degree mean being higher than those without 23.7 65.9
40.3 49.9
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? 72.3 57.4
Your findings: I can conclude that different factors change the salaries for different people. Those with degrees make more on average. 66.2 56
The lecture's related findings: This just mean they are getting paid more because of education and experience. 61.7 68.1
Overall conclusion:
Why - what statistical results support this conclusion?
The results from question 3 supports my claims. More reseach needs to be done to determine if it is really equal pay for equal work.
Or is it that they are getting rewarded for the education they have on top of the experience, which plays a factot(sometimes).

Sheet1

Salary
Male Femael
54.5 34.1
28.3 41.4
60.9 22.8
49.2 23.3
74.1 24.3
73 41.8
59.7 25
48.5 22.6
23.9 63.1
78.9 36.2
23.6 35.5
46.2 57.6
75.6 22.2
47.5 53.4
28.1 22.3
63.7 74.4
26.9 22.9
64.6 22.7
23.7 24.4
40.3 23.8
65.9 37.3
57.4 24.4
56 72.3
66.2 49.9
61.7 68.1

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 Sum
Step 4: Decision rule: Male 0
Step 5: Conduct the test - place test function in cell K54 Female 0
Sum: 0 0 0 0 0 0 0
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 0
Why? Female 0
What is your conclusion about the means in the population for male and female salaries? Sum: 0 0 0 0 0 0 0
4 What implications do this week's analysis have for our equal pay question?
Your findings:
The lecture's related findings:
Overall conclusion:
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 all of the variables used in Q1. Add the
two dummy variables - gender and education - to your list of independent variables. 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 salary 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 salary?
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 salary 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?
Your findings:
The lecture's related findings:
Overall conclusion:
5 What does regression analysis show us about analyzing complex measures?