BUS 308 Statistics for Managers

profilePossumJenkins
CopyofStudent_Assignment_File.11.01.201643.xlsx
Home>Mathematics homework help>Statistics homework help>BUS 308 Statistics for Managers

Data

ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Gr Copy Employee Data set to this page.
8 22.1 0.962 23 32 90 9 1 5.8 1 F A 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)?
15 22.6 0.984 23 32 80 8 1 4.9 1 F A Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
35 22.6 0.984 23 23 90 4 1 5.3 0 F A
37 23 0.999 23 22 95 2 1 6.2 0 F A The column labels in the table mean:
10 23.1 1.003 23 30 80 7 1 4.7 1 F A ID – Employee sample number Salary – Salary in thousands
23 23.1 1.004 23 36 65 6 1 3.3 0 F A Age – Age in years Performance Rating – Appraisal rating (Employee evaluation score)
11 23.3 1.012 23 41 100 19 1 4.8 1 F A SERvice – Years of service Gender: 0 = male, 1 = female
26 23.5 1.020 23 22 95 2 1 6.2 0 F A Midpoint – salary grade midpoint Raise – percent of last raise
31 23.6 1.028 23 29 60 4 1 3.9 1 F A Grade – job/pay grade Degree (0= BS\BA 1 = MS)
36 23.6 1.026 23 27 75 3 1 4.3 0 F A Gender1 (Male or Female) Compa-ratio - salary divided by midpoint
40 23.8 1.034 23 24 90 2 0 6.3 0 M A
14 24 1.045 23 32 90 12 1 6 1 F A
42 24.2 1.051 23 32 100 8 1 5.7 1 F A
19 24.3 1.055 23 32 85 1 0 4.6 1 M A
25 25 1.087 23 41 70 4 0 4 0 M A
32 26.5 0.855 31 25 95 4 0 5.6 0 M B
2 27.7 0.895 31 52 80 7 0 3.9 0 M B
34 28.6 0.923 31 26 80 2 0 4.9 1 M B
39 33.9 1.094 31 27 90 6 1 5.5 0 F B
20 34.1 1.101 31 44 70 16 1 4.8 0 F B
18 34.5 1.113 31 31 80 11 1 5.6 0 F B
3 35.1 1.132 31 30 75 5 1 3.6 1 F B
13 41.1 1.027 40 30 100 2 1 4.7 0 F C
7 41.3 1.032 40 32 100 8 1 5.7 1 F C
16 42.2 1.054 40 44 90 4 0 5.7 0 M C
41 45.8 1.144 40 25 80 5 0 4.3 0 M C
27 46.9 1.172 40 35 80 7 0 3.9 1 M C
5 48.2 1.004 48 36 90 16 0 5.7 1 M D
30 49.3 1.027 48 45 90 18 0 4.3 0 M D
24 56.3 1.173 48 30 75 9 1 3.8 0 F D
45 56.9 1.185 48 36 95 8 1 5.2 1 F D
47 57.2 1.003 57 37 95 5 0 5.5 1 M E
33 57.5 1.008 57 35 90 9 0 5.5 1 M E
4 58 1.018 57 42 100 16 0 5.5 1 M E
38 58.8 1.032 57 45 95 11 0 4.5 0 M E
50 59.6 1.046 57 38 80 12 0 4.6 0 M E
46 60.2 1.057 57 39 75 20 0 3.9 1 M E
22 60.3 1.257 48 48 65 6 1 3.8 1 F D
1 61.6 1.081 57 34 85 8 0 5.7 0 M E
44 61.8 1.085 57 45 90 16 0 5.2 1 M E
49 63 1.105 57 41 95 21 0 6.6 0 M E
17 63.7 1.118 57 27 55 3 1 3 1 F E
12 64.7 1.135 57 52 95 22 0 4.5 0 M E
48 69.5 1.219 57 34 90 11 1 5.3 1 F E
9 73.9 1.103 67 49 100 10 0 4 1 M F
43 75.6 1.128 67 42 95 20 1 5.5 0 F F
29 76.3 1.139 67 52 95 5 0 5.4 0 M F
21 77.2 1.152 67 43 95 13 0 6.3 1 M F
6 78.1 1.165 67 36 70 12 0 4.5 1 M F
28 78.3 1.169 67 44 95 9 1 4.4 0 F F

Week 2

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 over to this Assignment file.
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 tab, selecting Move or Copy, and copying the entire sheet to this file
(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 you do will not disrupt the original data values and relationships.
To Ensure full credit for each question, you need to show how you got your results. For example, Question 1 asks for several data values. If you obtain them using descriptive statistics,
then the cells should have an "=XX" formula in them, where XX is the column and row number showing the value in the descriptive statistics table. If you choose to generate each
value using fxfunctions, then each function should be located in the cell and the location of the data values should be shown.
So, Cell D31 - as an example - shoud contain something like "=T6" or "=average(T2:T26)". Having only a numerical value will not earn full credit.
The reason for this is to allow instructors to provide feedback on Excel tools if the answers are not correct - we need to see how the results were obtained.
In starting the analysis on a research question, we focus on overall descriptive statistics and seeing if differences exist. Probing into reasons and mitigating factors is a follow-up activity.
1 The first step in analyzing data sets is to find some summary descriptive statistics for key variables. Since the assignment problems will
focus mostly on the compa-ratios, we need to find the mean, standard deviations, and range for our groups: Males, Females, and Overall.
Sorting the compa-ratios into male and females will require you copy and paste the Compa-ratio and Gender1 columns, and then sort on Gender1.
The values for age, performance rating, and service are provided for you for future use, and - if desired - to test your approach to the compa-ratio answers
(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 from Descriptive Statistics.
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 data (Example: =average(T2:T51)
Compa-ratio Age Perf. Rat. Service
Overall Mean 1.0690 35.7 85.9 9.0
Standard Deviation 0.0011 8.2513 11.4147 5.7177 Note - remember the data is a sample from the larger company population
Range 0.402 30 45 21
Female Mean 1.0723 32.5 84.2 7.9
Standard Deviation 0.0167 6.9 13.6 4.9
Range 0.295 26.0 45.0 18.0
Male Mean 1.0541 38.9 87.6 10.0
Standard Deviation 0.0169 8.4 8.7 6.4
Range 0.317 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: Probability
a.       Randomly selected person being in grade E or above? 0.88
b.      Randomly selected person being a male in grade E or above? 0.4
c.      Randomly selected male being in grade E or above? 0.84
d. Why are the results different?
The probability of randomly selecting male takes into focus whole population less those who got grade F while the probability of randomly selecting male takes into focus only the male population of those who scored E grade and above.
The probability of a selected person being grade E or above takes into account the probability of all grades less grade F
3 Normal Curve based probability: For each group (overall, females, males), what are the values for each question below?:
Make sure your answer cells show the Excel function and cell location of the data used.
A 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 the top 1/3 of the range,
For the overall group, this would be the 50/3 or 17th (rounded), for the gender groups, it would be the 25/3 = 8th (rounded) value.
Overall Female Male All of the functions below are in the fx statistical list.
i. How nany salaries are in the top 1/3 (rounded to nearest whole number) for each group? 60.6 41.9 62.83 Use the "=ROUND" function (found in Math or All list)
ii What Compa-ratio value starts the top 1/3 of the range for each group? 1.108 1.104 1.111 Use the "=LARGE" function
iii What is the z-score for this value? 0.76634 0.187227 0.558967 Use Excel's STANDARDIZE function
iv. What is the normal curve probability of exceeding this score? 0.6071 0.1651 0.1361369 Use "=1-NORM.S.DIST" function
B How do you interpret the relationship between the data sets? What does this suggest about our equal pay for equal work question?
Based on Compa results, the value that cuts off the top third salary value is almost the same.
The information provided in this case is not sufficient to make conclusion regarding equal pay
4 Based on our sample data set, can the male and female compa-ratios in the population be equal to each other?
A 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: Male and female compa ratios in the population are equal to each other
Ha: Male and female compa ratios in the population are not equal to each other
Step 2: Decision Rule: Reject Ho if P<0.05
Step 3: Statistical test: Two sample t test
Why? There is need to determine if these two groups have equal variances.
Step 4: Conduct the test - place cell B77 in the output location box.
t-Test: Two-Sample Assuming Equal Variances
Male Female
Mean 1.05516 1.07464
Variance 0.00657189 0.00655624
Observations 25 25
Pooled Variance 0.006564065
. Hypothesized Mean Difference 0
df 48
t Stat -0.850075545
P(T<=t) one-tail 0.1997517452
t Critical one-tail 1.6772241961
P(T<=t) two-tail 0.3995034904
t Critical two-tail 2.0106347576
Step 5: Conclusion and Interpretation
What is the p-value: 0.3995
Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? No
What is your decision: REJ or NOT reject the null? Not Reject the null
What does this result say about our question of variance equality? there exists statitically significant differenct in male and female compa
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: Male Compa ratio =Female Compa ratio
Ha: Male Compa ratio =/=Female Compa ratio
Step 2: Decision Rule: Reject Ho if P<0.05
Step 3: Statistical test: Analysis of variance
Why? Aims to determine the existing difference between the male and female average
Step 4: Conduct the test - place cell B109 in the output location box.
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Compa 50 53.245 1.0649 0.0065269082
Gender 50 25 0.5 0.2551020408
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 7.97780025 1 7.97780025 60.9856079086 0 3.938111078
Within Groups 12.8198185 98 0.1308144745
Total 20.79761875 99
Step 5: Conclusion and Interpretation
What is the p-value: 0
Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)? Yes
What is your decision: REJ or NOT reject the null? Reject
What does your decision on rejecting the null hypothesis mean?
the mean are not equal between male and female compa ratio
If the null hypothesis was rejected, calculate the effect size value:
0.24
If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected?
The effect of size is less than 0.5 thus indicating there is a small effect on the sample in identifying the difference
What does the result of this test tell us about our question on salary equality?
There is difference between the male and female salaries
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 midpoint (which is 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: Female average compa-ratio equal to or less than the midpoint value of 1.00
Ha: Female average compa-ratio is not equal to the midpoint value of 1.00
Step 2: Decision Rule: Reject Ho if P<0.05
Step 3: Statistical test: One sample t test
Why? focuses on determining whether female average is less or equal to 1
Step 4: Conduct the test - place cell B162 in the output location box.
t-Test: Two-Sample Assuming Equal Variances
Variable 1 Variable 2
Mean 1.07464 1
Variance 0.00655624 0
Observations 25 25
Pooled Variance 0.00327812
Hypothesized Mean Difference 0
df 48
t Stat 4.6090796525
P(T<=t) one-tail 0.0000150462
t Critical one-tail 1.6772241961
P(T<=t) two-tail 0.0000300925
t Critical two-tail 2.0106347576
Step 5: Conclusion and Interpretation
What is the p-value: 0.0000150462
Is the P-value < 0.05 (for a one tail test) or 0.025 (for a two tail test)?
Yes
What, besides the p-value, needs to be considered with a one tail test?
t statistic
Decision: Reject or do not reject Ho? reject
What does your decision on rejecting the null hypothesis mean?
Female average compa-ratio is not equal to the midpoint value of 1.00
If the null hypothesis was rejected, calculate the effect size value:
1.3
If the effect size was calculated, what doe the result mean in terms of why the null hypothesis was rejected?
The effect of size is greater than 1 thus indicating there is a very large effect on the sample in identifying the difference
What does the result of this test tell us about our question on salary equality?
the female compa ratio is not less or equal to 1
6 Considering both the salary information in the lectures and your compa-ratio information, what conclusions can you reach about equal pay for equal work?
Compa shows that the salaries are almost the same and the difference between them is negligible although there is no equal pay for equal work
Why - what statistical results support this conclusion?
the two sample test and analysis of variance conducted shows clearly that there is difference in salaries between men and women

Week 3

Week 3 ANOVA Three Questions
Remember to show how you got your results in the appropriate cells. For questions using functions, show the input range when asked.
Group name: G1 G2 G3 G4 G5 G6
1 One interesting question is are the average compa-ratios equal across salary ranges of 10K each. Salary Intervals: 22-29 30-39 40-49 50-59 60-69 70-79
While compa-ratios remove the impact of grade on salaries, are they different for different pay levels, Compa-ratio values: 0.962 1.094 1.027 1.173 1.057 1.103
that is are people at different levels paid differently relative to the midpoint? (Put data values at right.) 0.984 1.101 1.032 1.185 1.257 1.128
0.984 1.113 1.054 1.003 1.081 1.139
What is the data input ranged used for this question: 0.999 1.132 1.144 1.008 1.085 1.152
Step 1: Ho: Compa ratios are equal 1.003 1.172 1.018 1.105 1.165
Ha: Compa ratios are unequal 1.004 1.004 1.032 1.118 1.169
Step 2: Decision Rule: Reject Ho if P<0.05 1.012 1.027 1.046 1.135
Step 3: Statistical test: Single fact Anova 1.020 1.219
Why? Aims to determine the diffrence in compa variable based on salary groups 1.028
Step 4: Conduct the test - place cell b16 in the output location box. 1.026
Anova: Single Factor 1.034
1.045
SUMMARY 1.051
Groups Count Sum Average Variance 1.055
G1 18 17.967 0.9981666667 0.0034282647 1.087
G2 4 4.44 1.11 0.0002766667 0.855
G3 7 7.46 1.0657142857 0.0042509048 0.895
G4 7 7.465 1.0664285714 0.006133619 0.923
G5 8 9.057 1.132125 0.0049375536
G6 6 6.856 1.1426666667 0.0006162667
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 0.1607566488 5 0.0321513298 8.8937636456 0.0000067936 2.4270401198
Within Groups 0.1590618512 44 0.0036150421
Total 0.3198185 49
Step 5: Conclusions and Interpretation
What is the p-value? 0.0000067936
Is P-value < 0.05? Yes
What is your decision: REJ or NOT reject the null? Reject the null hypothesis
If the null hypothesis was rejected, what is the effect size value (eta squared)? 0.5026496241
If calculated, what does the effect size value tell us about why the null hypothesis was rejected? There is a large effect size which shows that the rejection of null hypothesis was caused by variable interaction
What does that decision mean in terms of our equal pay question? There exist significant difference in pay
2 If the null hypothesis in question 1 was rejected, which pairs of means differ? Why?
Groups Compared Diff T +/- Term Low to High Difference Significant? Why?
G1 G2 -0.1118333333 2.015 0.0669812904 -0.1788146237 -0.044852043 yes Zero not in rage
G1 G3 -1.0657142857 2.015 0.0539750619 -1.1196893477 -1.0117392238 yes Zero not in rage
G1 G4 -0.0682619048 2.015 0.0539750619 -0.1222369667 -0.0142868428 yes Zero not in rage
G1 G5 -0.1339583333 2.015 0.0514889275 -0.1854472608 -0.0824694058 yes Zero not in rage
G1 G6 -0.1445 2.015 0.0571218364 -0.2016218364 -0.0873781636 yes Zero not in rage
G2 G3 0.0442857143 2.015 0.0759496444 -0.0316639301 0.1202353586 no Zero in range
G2 G4 0.0435714286 2.015 0.0759496444 -0.0323782158 0.1195210729 no Zero in range
G2 G5 -0.022125 2.015 0.0742034421 -0.0963284421 0.0520784421 no Zero in range
G2 G6 -0.0326666667 2.015 0.0782172958 -0.1108839624 0.0455506291 no Zero in range
G3 G4 -0.0007142857 2.015 0.0647700743 -0.0654843601 0.0640557886 no Zero in range
G3 G5 -0.0664107143 2.015 0.0627133548 -0.1291240691 -0.0036973595 Yes Zero not in range
G3 G6 -0.076952381 2.015 0.0674148308 -0.1443672117 -0.0095375502 yes Zero not in range
G4 G5 -0.0656964286 2.015 0.0627133548 -0.1284097834 -0.0029830738 yes Zero not in range
G4 G6 -0.0762380952 2.015 0.0674148308 -0.143652926 -0.0088232645 yes Zero not in range
G5 G6 -0.0105416667 2.015 0.0654412847 -0.0759829514 0.0548996181 yes Zero not in range
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?
Yes. These results provides an understanding on the existing difference in pay across the different salary ranges considered.
The information significantly reflects on the conclusion regarding equal pay for equal work done. Where from the analysis there is no equal pay among the groups

Week 4

Regression and Corellation Five Questions Compa-ratio Midpoint Age Performance Rating Service Raise Degree Gender
Remember to show how you got your results in the appropriate cells. For questions using functions, show the input range when asked.
1 Create a correlation table using Compa-ratio and the other interval level variables, except for Salary.
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? T = Significant r =
c Are there any surprises - correlations you though would be significant and are not, or non significant correlations you thought would be?
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 Q1 along with
including the dummy variables. Show the result, and interpret your findings by answering the following questions.
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: Midpoint Age Perf. Rat. Service Gender Degree
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:
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?