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Expert answer:Write a minimum 4 page report explaining the resul

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Answer & Explanation:Write a minimum 4 page report explaining the results from your analysis of the ROI of Business Majors and Engineering Majors. Use your results from each week’s assignment to make this report. This report should include:A detailed description of the data used in this analysis – specifically explain what the data in each column represents.A detailed explanation of any information learned about: School Type for each major; The Cost for each major;The 30 Year ROI for each major;The Annual % ROI for each major. Explanations should be supported with the results obtained from your work in previous weeks.Finally, answer the following questions and support your answer with your results. Does there appear to be a particular major that gives a better ROI?  Why or Why not? Given that we are using statistical inference to make our conclusions, is it guaranteed that the major you choose that gave a better ROI for this sample will always have a better ROI than the other major? Explain your reasoningI’ve included all previous analyses here to refer back to when completing this assignment.WEEK 1 ANALYSIS.docx WEEK 2 ANALYSIS.xlsx WEEK 3 ANALYSIS.xlsx WEEK 5 ANALYSIS.docx WEEK 6 ANALYSIS.docx WEEK 7 ANALYSIS.docx ROI_by_Major Week 4.xlsx  (Originl ROI spreadsheet)
week_1_analysis.docx

week_2_analysis.xlsx

week_3_analysis.xlsx

week_5_analysis.docx

week_6_analysis.docx

week_7_analysis.docx

roi_by_major_week_4.xlsx

Unformatted Attachment Preview

In the Business Major private schools over power the public school in the graph shown below:
Business Major
Private
Public
The Engineering Major shows that the private school sector is slightly higher than the public school
sector shown in the graph below:
Engineering Major
Private
Public
6.00%
6.50%
7.00%
7.50%
8.00%
8.50%
9.00%
9.50%
10.00%
10.50%
11.00%
More
Frequency
6.0%
6.5%
7.0%
7.5%
8.0%
8.5%
9.0%
9.5%
10.0%
10.5%
11.0%
More
Frequency
Histogram Engineering Major
10
5
0
Frequency
Bin
.
Histogram Business Major
8
6
4
2
0
Bin
Frequency
School Type
Private
Private
Private
Public
Private
Public
Private
Private
Private
Private
Private
Private
Private
Private
Private
Public
Public
Private
Private
Private
# of Private Schools:
# of Public Schools:
Total Schools:
Private schools with ROI between $1.5M & $1.8M:
Cost
$222,700.00
$176,400.00
$212,200.00
$125,100.00
$212,700.00
$92,910.00
$214,900.00
$217,800.00
$225,600.00
$217,300.00
$226,500.00
$215,500.00
$223,500.00
$226,600.00
$189,300.00
$89,700.00
$87,030.00
$218,200.00
$229,900.00
$148,800.00
16
4
20
30 Year ROI
$1,786,000.00
$1,758,000.00
$1,714,000.00
$1,535,000.00
$1,529,000.00
$1,501,000.00
$1,485,000.00
$1,483,000.00
$1,444,000.00
$1,442,000.00
$1,441,000.00
$1,438,000.00
$1,428,000.00
$1,414,000.00
$1,397,000.00
$1,382,000.00
$1,376,000.00
$1,343,000.00
$1,339,000.00
$1,321,000.00
Question 2:
4 divided by the total # of private schools = the
Question 3: Probability of Private school 30 year ROI bet
Annual ROI
7.70%
8.40%
7.80%
9.10%
7.40%
10.10%
7.30%
7.20%
7.00%
7.10%
7.00%
7.20%
7.00%
7.00%
7.50%
9.90%
10.00%
6.90%
6.70%
8.10%
Probability of Private school for Business Major = 16/20
Probability of Public school for Business Major = 4/20
or
or
80%
20%
d by the total # of private schools = the probability
bility of Private school 30 year ROI between $1.5M & $1.8M = 4/16
or
25%
School Type
Private
Private
Private
Private
Private
Private
Private
Private
Private
Private
Private
# of Private Schools:
# of Public Schools:
Total Schools:
Cost
$221,700.00
$213,000.00
$230,100.00
$222,600.00
$225,800.00
$224,900.00
$221,600.00
$215,700.00
$217,800.00
$229,600.00
$219,400.00
11
9
20
30 Year ROI
Annual ROI
$2,412,000.00
8.70%
$2,064,000.00
8.30%
$1,949,000.00
7.90%
$1,947,000.00
8.00%
$1,938,000.00
8.00%
$1,915,000.00
7.90%
$1,878,000.00
7.90%
$1,794,000.00
7.90%
$1,752,000.00
7.70%
$1,716,000.00
7.50%
$1,676,000.00
7.60%
Question 2: Probability of Private school for Engineering
Probability of Public school for Engineering M
Private schools with ROI between $1.5M & $1.8M:
4 divided by the total # of private schools = the probability
Question 3: Probability of Private school 30 year ROI between $1.5M & $
or
or
55%
45%
or
36.36%
School Type
Private
Private
Private
Public
Private
Public
Private
Private
Private
Private
Private
Private
Private
Private
Private
Public
Public
Private
Private
Private
Best College ROI by Majo 2013: Payscale.com
# of Private Schools:
# of Public Schools:
Total Schools:
Private schools with ROI between $1.5M & $1.8M:
Cost
$222,700.00
$176,400.00
$212,200.00
$125,100.00
$212,700.00
$92,910.00
$214,900.00
$217,800.00
$225,600.00
$217,300.00
$226,500.00
$215,500.00
$223,500.00
$226,600.00
$189,300.00
$89,700.00
$87,030.00
$218,200.00
$229,900.00
$148,800.00
16
4
20
30 Year ROI
$1,786,000.00
$1,758,000.00
$1,714,000.00
$1,535,000.00
$1,529,000.00
$1,501,000.00
$1,485,000.00
$1,483,000.00
$1,444,000.00
$1,442,000.00
$1,441,000.00
$1,438,000.00
$1,428,000.00
$1,414,000.00
$1,397,000.00
$1,382,000.00
$1,376,000.00
$1,343,000.00
$1,339,000.00
$1,321,000.00
Question 2:
4 divided by the total # of private schools = the
Question 3: Probability of Private school 30 year ROI bet
Annual ROI
6.70%
6.90%
7.00%
7.00%
7.00%
7.00%
7.10%
7.20%
7.20%
7.30%
7.40%
7.50%
7.70%
7.80%
8.10%
8.40%
9.10%
9.90%
10.00%
10.10%
1.564
Standard Deviation
Mean
Median
0.010995693
7.82%
7.35%
Annual ROI %
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
Probability of Private school for Business Major = 16/20
Probability of Public school for Business Major = 4/20
or
or
80%
20%
d by the total # of private schools = the probability
bility of Private school 30 year ROI between $1.5M & $1.8M = 4/16
or
25%
19 20
School Type
Private
Private
Private
Private
Private
Public
Private
Private
Public
Private
Public
Private
Public
Private
Public
Public
Public
Public
Private
Public
# of Private Schools:
# of Public Schools:
Total Schools:
Cost
$221,700.00
$213,000.00
$230,100.00
$222,600.00
$225,800.00
$87,660.00
$224,900.00
$221,600.00
$125,100.00
$215,700.00
$92,530.00
$217,800.00
$89,700.00
$229,600.00
$101,500.00
$115,500.00
$104,500.00
$69,980.00
$219,400.00
$64,930.00
11
9
20
30 Year ROI
Annual ROI
$2,412,000.00
8.70%
$2,064,000.00
8.30%
$1,949,000.00
7.90%
$1,947,000.00
8.00%
$1,938,000.00
8.00%
$1,937,000.00
11.20%
$1,915,000.00
7.90%
$1,878,000.00
7.90%
$1,854,000.00
9.80%
$1,794,000.00
7.90%
$1,761,000.00
10.60%
$1,752,000.00
7.70%
$1,727,000.00
10.70%
$1,716,000.00
7.50%
$1,703,000.00
10.20%
$1,694,000.00
9.70%
$1,690,000.00
10.10%
$1,685,000.00
11.50%
$1,676,000.00
7.60%
$1,668,000.00
11.70%
Standard Deviation
14.00%
12.00%
10.00%
Question 2: Probability of Private school for Engineering
Probability of Public school for Engineering M
Private schools with ROI between $1.5M & $1.8M:
4 divided by the total # of private schools = the probability
Question 3: Probability of Private school 30 year ROI between $1.5M & $
Standard Deviation
Mean
Median
0.01367
9.01%
8.30%
Annual ROI %
14.00%
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
of Private school for Engineering Major = 11/20 or
of Public school for Engineering Major = 9/20
or
ate schools = the probability
30 year ROI between $1.5M & $1.8M = 4/11
or
55%
45%
36.36%
Q1) For each of the 2 majors consider the ‘School Type’ column. Assuming the
requirements are met, construct a 90% confidence interval for the proportion of the schools
that are ‘Private’. Be sure to interpret your results.
Case 1:
Critical value for 90% confidence interval,z =1.645
Business Major
We have the total school =20
Total private school =16
Proportion of school that are private =16/2 0=.8
Mean,m=.8
Standard error,s=sqrt(p(1-p)/n)=sqrt(.8*.2/20)=.08944
Confidence interval is =>
Lower limit =m-z*s=>.8-1.645*.08944=.653
Upper limit=m+z*s =>.8+1.645*.08944=>.947
The 90% confidence interval is (.653,.947)
Interpretation:We are 90% confident that the private college of the sample lies in the
proportion of .653 to .947 of the whole private college(population)
Engineering Major
Total school=20
Private school=11
Proportion of school,mean,m=11/20=.55
Standard error,s=sqrt(p*(1-p)/n)=sqrt(.55*.45/20)=.1112429
Lower limit =m-z*s =>.55-1.645*.1112429= .367
Upper limit =>m+z*s =>.55+1.645*.1112429=.733
The 90% confidence interval is (.367,.733)
Interpretation: We are 90% confident that the private college of the sample lies in the
proportion of .653 to .947 of the whole private college(population)
2) Calculate the mean of the ROI for each of the Business Major and Engineering Major
Critical value for 95% confidence interval is 1.96
BUSINESS MAJOR
Mean,m=Sum of all annual ROI/20 =7.82%=.0782
Standard error,S=standard deviation/sqrtn =.01099/sqrt20 =.002458
Confidence Interval
Lower limit=m-z*s =>.0782-1.96*.002458=>.073=7.3%
Upper limit =>m+z*s =>.0782+1.96*.002458=>.083=8.3%
Thus the confidence interval is (7.3%,8.3%)
Interpretation: -We are 95% confident that the annual ROI on Business Major is between
7.3% and 8.3%.
ENGINEERING MAJOR
Mean of ROI =9.145% =.091455
Standard error,s=Standard deviation/sqrt20 =.0146/sqrt20 =.003265
Confidence interval
Lower => .09145-1.96*.003265=.08775 =8.5%
Upper =>.09145+1.96*.003265=.0978=9.78%
The 95% confidence interval is (8.8%,9.8%)
Interpretation: -We are 95% confident that the annual ROI on Business Major is between
8.5% and 10.1%.
Business Statistics
Project Week 6
Using the ROI data set:
1. For each of the 2 majors test the hypothesis at the 5% significance level:
o The mean ‘Cost’ for a college is $160,000. Be sure to interpret your results.
Business major:
Mean
Variance
Observations
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Cost 188632 2550596343 20 0 19 2.535396094 0.01008694 1.729132812 0.020173879 2.093024054 test 160000 0 20 Since P(T<=t) two-tail = 0.020173879 < 0.05, so we should reject the null hypothesis, that is to say, the mean ‘Cost’ for Business major is not $160,000. Engineering major: Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Cost 164680 4406984411 20 0 19 0.31527541 0.37799454 1.72913281 0.75598907 2.09302405 test 160000 0 20 Since P(T<=t) two-tail = 0.75598907>0.05, so we should can not reject the null hypothesis, that is to say, the
mean ‘Cost’ for Engineering major is $160,000.
2. For Business versus Engineering majors conduct a two sample test of the hypothesis at
the 10% significance level (assume the variances are not equal):
o The average ’30-Year ROI’ for Business majors is less than for Engineering Majors. Be
sure to interpret your results.
t-Test: Two-Sample Assuming Unequal Variances
Mean
Variance
Observations
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 30 Year ROI Business 1477800 17673957895 20 0 35 -7.203889288 1.04423E-08 1.306211802 2.08847E-08 1.689572458 30 Year ROI Engineering 1838000 32327578947 20 Since P(T<=t) one-tail = 1.04423E-08<0.1, so we can not reject the null hypothesis, that is to say, the average ’30-Year ROI’ for Business majors is less than for Engineering Majors. Business Statistics Project 1. 2. y ̂ = 12.678 – 0.00002X r2=0.9515 3. 4. Calculate the estimated ‘Annual % ROI’ when the ‘Cost’ (X) is $160,000. Y= 12.678 – 0.00002*160,000= 9.478% 5. Rejected the null hypothesis. SUMMARY OUTPUT Regression Statistics Multiple R 0.97543117 R Square 0.951465967 Adjusted R Square 0.948769632 Standard Error 0.330495369 Observations 20 ANOVA df Regression Residual Total Intercept Cost 1 18 19 SS 38.5434106 1.966089398 40.5095 MS F Significance F 38.5434106 352.8737765 2.83396E-13 0.109227189 Coefficients Standard Error t Stat 12.67820122 0.202084296 62.73719176 -2.1455E-05 1.14214E-06 -18.78493483 P-value 1.56075E-22 2.83396E-13 Lower 95% 12.25363787 -2.38545E-05 Upper 95% 13.10276457 -1.90554E-05 Lower 95.0% Upper 95.0% 12.25363787 13.10276457 -2.38545E-05 -1.90554E-05 6. Write a paragraph or more on any observations you make about the regression estimates, coefficient of determination, the plots, and the results of your hypothesis tests. The regression estimates function is Annual % ROI= 12.678 – 0.00002* Cost. The coefficient of determination is 0.948769632. The plot is drew as above, and we should reject the null hypothesis, for P<0.05. School Type Private Private Private Public Private Public Private Private Private Private Private Private Private Private Private Public Public Private Private Private Best College ROI by Majo 2013: Payscale.com # of Private Schools: # of Public Schools: Total Schools: Private schools with ROI between $1.5M & $1.8M: Cost $222,700.00 $176,400.00 $212,200.00 $125,100.00 $212,700.00 $92,910.00 $214,900.00 $217,800.00 $225,600.00 $217,300.00 $226,500.00 $215,500.00 $223,500.00 $226,600.00 $189,300.00 $89,700.00 $87,030.00 $218,200.00 $229,900.00 $148,800.00 16 4 20 30 Year ROI $1,786,000.00 $1,758,000.00 $1,714,000.00 $1,535,000.00 $1,529,000.00 $1,501,000.00 $1,485,000.00 $1,483,000.00 $1,444,000.00 $1,442,000.00 $1,441,000.00 $1,438,000.00 $1,428,000.00 $1,414,000.00 $1,397,000.00 $1,382,000.00 $1,376,000.00 $1,343,000.00 $1,339,000.00 $1,321,000.00 Question 2: 4 divided by the total # of private schools = the Question 3: Probability of Private school 30 year ROI bet Annual ROI 6.70% 6.90% 7.00% 7.00% 7.00% 7.00% 7.10% 7.20% 7.20% 7.30% 7.40% 7.50% 7.70% 7.80% 8.10% 8.40% 9.10% 9.90% 10.00% 10.10% 1.564 Standard Deviation Mean Median 0.010995693 7.82% 7.35% Annual ROI % 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Probability of Private school for Business Major = 16/20 Probability of Public school for Business Major = 4/20 or or 80% 20% d by the total # of private schools = the probability bility of Private school 30 year ROI between $1.5M & $1.8M = 4/16 or 25% 19 20 School Type Private Private Private Private Private Public Private Private Public Private Public Private Public Private Public Public Public Public Private Public # of Private Schools: # of Public Schools: Total Schools: Cost $221,700.00 $213,000.00 $230,100.00 $222,600.00 $225,800.00 $87,660.00 $224,900.00 $221,600.00 $125,100.00 $215,700.00 $92,530.00 $217,800.00 $89,700.00 $229,600.00 $101,500.00 $115,500.00 $104,500.00 $69,980.00 $219,400.00 $64,930.00 11 9 20 30 Year ROI Annual ROI $2,412,000.00 8.70% $2,064,000.00 8.30% $1,949,000.00 7.90% $1,947,000.00 8.00% $1,938,000.00 8.00% $1,937,000.00 11.20% $1,915,000.00 7.90% $1,878,000.00 7.90% $1,854,000.00 9.80% $1,794,000.00 7.90% $1,761,000.00 10.60% $1,752,000.00 7.70% $1,727,000.00 10.70% $1,716,000.00 7.50% $1,703,000.00 10.20% $1,694,000.00 9.70% $1,690,000.00 10.10% $1,685,000.00 11.50% $1,676,000.00 7.60% $1,668,000.00 11.70% Standard Deviation 14.00% 12.00% 10.00% Question 2: Probability of Private school for Engineering Probability of Public school for Engineering M Private schools with ROI between $1.5M & $1.8M: 4 divided by the total # of private schools = the probability Question 3: Probability of Private school 30 year ROI between $1.5M & $ Standard Deviation Mean Median 0.01367 9.01% 8.30% Annual ROI % 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 of Private school for Engineering Major = 11/20 or of Public school for Engineering Major = 9/20 or ate schools = the probability 30 year ROI between $1.5M & $1.8M = 4/11 or 55% 45% 36.36% ... Purchase answer to see full attachment

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