Final Project week 8 for Business/Math Statistics

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Final Project Week 8

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 reasoning

PREVIOUS WEEKS WORK IS ATTACHED.

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Frequency 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 Solution 30 Year ROI Annual ROI $1,786,000.00 7.70% $1,758,000.00 8.40% $1,714,000.00 7.80% $1,535,000.00 9.10% $1,529,000.00 7.40% $1,501,000.00 10.10% $1,485,000.00 7.30% $1,483,000.00 7.20% $1,444,000.00 7.00% $1,442,000.00 7.10% $1,441,000.00 7.00% $1,438,000.00 7.20% $1,428,000.00 7.00% $1,414,000.00 7.00% $1,397,000.00 7.50% $1,382,000.00 9.90% $1,376,000.00 10.00% $1,343,000.00 6.90% $1,339,000.00 6.70% $1,321,000.00 8.10% 7 6 5 Frequency School Type Private Private Private Public Private Public Private Private Private Private Private Private Private Private Private Public Public Private Private Private 1 0 Number of schools 4 School Type Private Public 16 Values Answers: 20% of schools are public 80% of schools are private Business major is the majority Bin 0-6.00% 6.01%-6.50% Number of Schools 16 4 20 Frequency 0 0 Percentage 80.00% 20.00% 100.00% 1 2 3 2 Number of Schools Percentage School Type Private Public Grand Total 4 Upper Range 6.00% 6.50% 7.00% 7.50% 8.00% 8.50% 9.00% 6.51%-7.00% 7.01%-7.50% 7.51%-8.00% 8.01%-8.50% 8.51%-9.00% 9.01%-9.50% 9.51%-10.00% 10.01%-10.50% 10.51%-11.00% 11%+ 6 6 2 2 0 1 2 1 0 0 9.50% 10.00% 10.50% 11.00% Histogram Business Major: Annual % ROI 7 6 Frequency 5 4 3 2 Frequency 1 0 Bin Anwer Business Major give an annual % ROI in 6.5% and 7.5%, within the majority of schools. Max ROI is lower than 11% All schools have ROI at least 6% Frequency 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 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% Number of schools Percentage Number of schools Histogram Engineer 9 8 7 6 5 4 3 2 1 0 School Type Private 9 11 Values 1 Frequency School Type Private Private Private Private Private Public Private Private Public Private Public Private Public Private Public Public Public Public Private Public Public Answer: 7.5% and 8% ROI in most schools who o A large amoung offer more than 11% RO The shows that zero schools has less tha Solution School Type Private Public Grand Total Number of schools 11 9 20 Percentage 55.00% 45.00% 100.00% 2 Comments: Private schools account for 55% of schools Public schools account for 45% of schools Histogram Engineering Major: Annual % ROI Frequency Bin 7.5% and 8% ROI in most schools who offer Engineering as a Major A large amoung offer more than 11% ROI The shows that zero schools has less than 7% ROI Upper Range 6.00% 6.50% 7.00% 7.50% 8.00% 8.50% 9.00% 9.50% 10.00% 10.50% 11.00% Bin 0-6.00% 6.01%-6.50% 6.51%-7.00% 7.01%-7.50% 7.51%-8.00% 8.01%-8.50% 8.51%-9.00% 9.01%-9.50% 9.51%-10.00% 10.01%-10.50% 10.51%-11.00% 11%+ Frequency 0 0 0 1 8 1 1 0 2 2 2 3 Nicki Worthy MAT315 Week 3 Project: 1. If we select 7 colleges from a major and then record whether they are of ‘School Type’ ‘Private’ or not, are this experiment a binomial one? Why or why not? I believe that it is a binomial because the following conditions are met; observations are fixed, possibility of failure and success exists. Each experiment is independent of each other. Since the histograms shape is not bell-shaped about the mean, annual ROI is not normally distributed. Mean= 182.9/20= 9.145 Median= (8.3+8.7)/2=8.5 Engineering Histogram 14 12 10 8 6 4 2 0 1 2 3 4 5 6 7 8 9 10 11 annual ROI 12 13 14 15 16 17 18 19 20 2. For each of the 2 majors determine if the ‘Annual % ROI’ appears to be normally distributed. Consider the shape of the histogram and the measures of central tendency (mean and median) to justify your results. Report on each of these with charts and calculations to justify your answers. Business Histogram 12 10 8 6 4 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 annual ROI The histograms shape is not bell-shaped about the mean therefore annual ROI is not usually distributed. Mean= 156.4/20=7.82 Median= (7.3+7.4)/2= 7.35 1. Population proportion confidence interval. P is given by; 𝑝𝑞 p±Z√ 𝑛 Where the sample proportion (p) is equal to the number of successes in the sample (x) divided by the number of trials n (n is the sample size) 𝑥 i.e. p = 𝑛 and q = 1-p Engineering major. 𝑥 11 x= 11, n=20, therefore p=𝑛 = 20 = 0.55 At 90% confidence interval the Z score from the normal distribution table is = 1.645 𝑝𝑞 0.55×0.45 The confidence interval is; p±Z√ 𝑛 = 0.55±1.645√ 20 = 0.55±1.645 (0.11124) = 0.55±0.183 = [0.367, 0.733] The proportion confidence interval is; 0.367< p< 0.733 Interpretation: we are 90% confident that from sample population, the proportion of the private schools range from 36.7% to 73.3% in the engineering major. Business major. 𝑥 16 x= 16, n=20, therefore p=𝑛 = 20 = 0.8 At 90% confidence interval the Z score from the normal distribution table is = 1.645 𝑝𝑞 0.8×0.2 The confidence interval is; p±Z√ 𝑛 = 0.8±1.645√ 20 = 0.8±1.645 (0.08944) = 0.8±0.147 = [0.653, 0.947] The proportion confidence interval is; 0.653< p< 0.947 Interpretation: we are 90% confident that from sample population, the proportion of the private schools range from 65.3% to 94.7% in the business major. 2. The mean for the ROI confidence interval. Engineering major. Since this is small sample the interval estimate is; point estimate ±t × S.E (standard error.) = X ±t× 𝑠 √𝑛 X = 9.145% S= 0.063647 N=20 T from the t-test statistic table with d.f = 20-1=19 =2.093 Confidence interval = X ±t× 𝑠 √𝑛 = 9.145 ±2.093× 0.063647 √20 = 9.145±0.0298 [9.1152, 9.1748] 9.1152< X< 9.1748 Interpretation: this means that we are 95% confident that the mean ROI percentage lies between 9.1152% and 9.1748% for the engineering major. Business major. Confidence interval = point estimate ±t × S.E (standard error.) = X ±t× 𝑠 √𝑛 X = 7.82% S= 0.23 N=20 T from the t-test statistic table with d.f = 20-1=19 =2.093 Confidence interval = X ±t× 𝑠 0.23 √ √20 = 7.82 ±2.093× 𝑛 = 7.82±0.1076 [7.7124, 7.9276] 7.7124< X< 7.9276 Interpretation: this means that we are 95% confident that the mean ROI percentage lies between 7.7124% and 7.9276% for the business major. 30 Year ROI(Business Major) 30 Year ROI(Engineering major ) $1,786,000.00 $2,412,000.00 $1,758,000.00 $2,064,000.00 $1,714,000.00 $1,949,000.00 $1,535,000.00 $1,947,000.00 $1,529,000.00 $1,938,000.00 $1,501,000.00 $1,937,000.00 $1,485,000.00 $1,915,000.00 $1,483,000.00 $1,878,000.00 $1,444,000.00 $1,854,000.00 $1,442,000.00 $1,794,000.00 $1,441,000.00 $1,761,000.00 $1,438,000.00 $1,752,000.00 $1,428,000.00 $1,727,000.00 $1,414,000.00 $1,716,000.00 $1,397,000.00 $1,703,000.00 $1,382,000.00 $1,694,000.00 $1,376,000.00 $1,690,000.00 $1,343,000.00 $1,685,000.00 $1,339,000.00 $1,676,000.00 $1,321,000.00 $1,668,000.00 Nicki Worthy t-Test: uneaqual valiance of two samples SD Mean Variance Observations Hypothesis Mean Difference df t-stat P(T>t) one tail t-critical one tail t critical two tail P(T>t) two tail Business Major(30 Year ROI) Engineering major( 30 years ROI 132943.4387 179798.7179 $1,477,800.00 $1,838,000.00 17673957895 3232757896 20 20 0 35 -7.203889288 0 1.3062 1.6896 0 The statistic test is negative. The significant level of 0.1 if greater that p-value (one tailed). So, the null hypothesis is rejected due to outcome that the average '30-year ROI' for Engineering Major is greater than the Business Major BUSINESS MAJOR (a) Scatter Diagram of Cost and ROI Scatter Diagram of Cost and Annual ROI 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% $0.00 $50,000.00 $100,000.00 $150,000.00 $200,000.00 $250,000.00 (b) Regression Equation and Coefficient of Determination The intercept (b0) in the regression equation of the Business Major School is 11.803987%, and coefficient of regression of the cost (b1) is - 0.0000211%. The intercept of 11.803987% shows the cost of the program the ROI of the business school is 11.803987%, and coefficient of regression of the cost of - 0.0000211% shows that if cost of the Business Major School increases by $1 then ROI is decreased by 0.0000211%. The coefficient of determination (r2) of the regression model is 0.9410. The coefficient of determination of 0.9410 shows that 94.10% variation of the ROI can be explained by the variation of the cost for the Business Major School. (c) Fitted Regression Line Fitted Regression Line Annual ROI (Y) 14.00 12.00 10.00 8.00 6.00 4.00 2.00 0.00 0.00 50,000.00 100,000.00 150,000.00 Cost (X) 200,000.00 250,000.00 (d) Estimated ‘Annual % ROI’ when the ‘Cost’ (X) is $160,000 For the given cost of $160000, the estimated ROI of the Business Major School is 8.427987%. Annual ROI (Y) = 11.803987 – (0.0000211*160000) = 8.427987% (e) Test of Hypothesis The regression coefficient of the program cost (b1) is statistically important as the p value of the coefficient of the program cost (
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Running head: FINAL PROJECT WEEK 8 FOR BUSINESS/MATH STATISTICS

FINAL PROJECT WEEK 8 FOR BUSINESS/MATH STATISTICS:
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FINAL PROJECT WEEK 8 FOR BUSINESS/MATH STATISTICS

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Introduction
A good education has always been equated to a better future. However, the rising cost of
education has ended up impacting negatively on the return on investment realized from having
attained a certain level of education in a particular major. In this research paper, the cost of
attaining an education in two types of schools by majoring in either business or engineering will
be compared to the ROI one realizes when they choose a particular major in a given school.
Description of data
Data used in the research study comprises of four variables which are school type, cost,
30 year ROI as well as annual ROI. The data set is divided into two groups that were as based on
which major a student chose. The two majors are the business major and the engineering major.
Firstly, variable school type has two types of schools, i.e. private schools and public
schools. Secondly, the cost variable contains data relating to the cost of attaining an education in
different types of schools and also relates to the major that was chosen by a student. Thirdly, the
variable 30-year ROI contains data about the return on investment in dollar amount a student
realizes after a thirty-year period. Just like data under the cost variable, 30-year R...


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