Running Head: WEEK 3 PROJECT 1 Week 3 Project Larry Morris Grantham University Online July 19, 2016 WEEK 3 PROJECT 2 Question 1 1. If we select 7 colleges from a major and then record whether they are of 'School Type' 'Private' or not, is this experiment a binomial one? Why or why not? Yes, it is a binomial experiment. It is a binomial experiment because it consists of the following: repeated trials; there are only two possible outcomes; probability of success, is the same on every trial; the outcome on one trial does not affect the outcome on the other one. Question 2 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. Engineering Major Histogram Histogram-Engineering Major 10 9 8 7 6 5 Frequency 4 3 2 1 0 7 8 9 11 12 More Annual % ROI Mean( Engineer ) 9.145 % and MedianEngineer 8.5 %. This Histogram is skewed to the right, and the corresponding shape is not bell-shape. The Annual ROI is not normally distributed. WEEK 3 PROJECT 3 Business Major Histogram Histogram-Business Major 14 12 10 8 Frequency 6 4 2 0 6 7 8 9 10 11 More Annual % ROI MedianBu sin ess 7.35 % and Mean( Bu sin ess ) 7.82 %. Histogram for Business Major is skewed to the right as well. The curve is not symmetric about the mean (mean= 7.82%), we can confidently conclude that based on the sampled data analyzed that the 'Annual % ROI' is not normally distributed. RUNNING HEADER: PROJECT WEEK 1 1 Business Statistics Project Week 1 Larry Morris July 5, 2016 RUNNING HEADER: PROJECT WEEK 1 2 Percentag e School Type Cost 30 Year ROI Annual ROI Cost 30 yr ROI Private $221,700.00 $2,412,000.00 8.70% $6.73 $6.56 Private $213,000.00 $2,064,000.00 8.30% $6.47 $5.61 Private $230,100.00 $1,949,000.00 7.90% $6.99 $5.30 Private $222,600.00 $1,947,000.00 8.00% $6.76 $5.30 Private $225,800.00 $1,938,000.00 8.00% $6.86 $5.27 Public $87,660.00 $1,937,000.00 11.20% $2.66 $5.27 Private $224,900.00 $1,915,000.00 7.90% $6.83 $5.21 Private $221,600.00 $1,878,000.00 7.90% $6.73 $5.11 Public $125,100.00 $1,854,000.00 9.80% $3.80 $5.04 Private $215,700.00 $1,794,000.00 7.90% $6.55 $4.88 Public $92,530.00 $1,761,000.00 10.60% $2.81 $4.79 Private $217,800.00 $1,752,000.00 7.70% $6.61 $4.77 Public $89,700.00 $1,727,000.00 10.70% $2.72 $4.70 Private $229,600.00 $1,716,000.00 7.50% $6.97 $4.67 Public $101,500.00 $1,703,000.00 10.20% $3.08 $4.63 Public $115,500.00 $1,694,000.00 9.70% $3.51 $4.61 Public $104,500.00 $1,690,000.00 10.10% $3.17 $4.60 Public $69,980.00 $1,685,000.00 11.50% $2.12 $4.58 Private $219,400.00 $1,676,000.00 7.60% $6.66 $4.56 Public $64,930.00 $1,668,000.00 11.70% $1.97 $4.54 $3,293,600.00 $36,760,000.00 $100.00 $100.00 RUNNING HEADER: PROJECT WEEK 1 3 Thus first proportional percentages are found out RUNNING HEADER: PROJECT WEEK 1 4 The frequency distribution and histogram using the column 'Annual % ROI' is Anual ROI Cost 30 Year ROI 66.5% 0.00 0.00 6.57% 0.00 0.00 77.5% 2,29,600.0 0 17,16,000.0 0 7.58% 1777900.0 0 14849000.0 0 88.5% 213000.00 2064000.00 8.59% 221700.00 2412000.00 99.5% 0 0 9.510% 240600.00 3548000.00 1010.5 % 206000.00 3393000.00 10.511% 182230.00 3488000.00 1111.5 % 157640.00 3622000.00 11.512% 64930.00 1668000.00 RUNNING HEADER: PROJECT WEEK 1 5 Running Head: Project Week 5 1 Project Week 5 Larry Morris Grantham University August 2, 2016 Running Head: Project Week 5 2 1. 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. We know that the 90% confidence interval for the population proportion is, 90% CI = ( ^p Z 0.05 ^p( 1 ^p ) n ) Where, ^p = the sample proportion Z 0.05 =1.645 and n = sample size. Thus from the given data we have the following. Business Major: ^p = 16/20 = 0.8 n = 20 Thus the 90% confidence interval for the population proportion of the schools that are 'Private' is, 90% CI = = (0.6529, ( 16 16 1 20 20 16 1.645 20 20 0.9471) ( ) ) Running Head: Project Week 5 3 Thus we are 90% confident that the population proportion of private schools among business major falls within the above confidence interval. Engineering Major: ^p = 11/20 = 0.55 n = 20 Thus the 90% confidence interval for the population proportion of the schools that are 'Private' is, 90% CI = = (0.3670, ( 0.55 1.645 0.55( 10.55 ) 20 ) 0.7330) Thus we are 90% confident that the population proportion of private schools among Engineering major falls within the above confidence interval. 2. For each of the 2 majors construct a 95% confidence interval for the mean of the column Annual % ROI'. Be sure to interpret your results. We know that the 95% confidence interval for the population mean is, Running Head: Project Week 5 4 Sample 95% CI = Sample mean Z 0.025Sample SD Where, Z 0.025 =1.96 Thus from the given data we have the following. Business Major: Sample mean = 7.82% Sample standard deviation = 1.0995693% Sample = 20 Thus the 95% confidence interval for the mean of the column 'Annual % ROI' is, Sample 95% CI = Sample mean Z 0.025Sample SD = (7.82 1.961.0995693 ) 20 = (7.3381%, 8.3019%) Thus we are 95% confident that the population mean of the column 'Annual % ROI' among business major falls within the above confidence interval. Engineering Major: Sample mean = 9.15% Sample standard deviation = 1.460164% Running Head: Project Week 5 5 Sample = 20 Thus the 95% confidence interval for the mean of the column 'Annual % ROI' is, Sample 95% CI = Sample mean Z 0.025Sample SD = (9.15 1.961.460164 ) 20 = (8.5101%, 9.7899%) Thus we are 95% confident that the population mean of the column 'Annual % ROI' among Engineering major falls within the above confidence interval. Running Head: PROJECT WEEK 2 1 Grantham University Business Statistics W2 Project Assignment Project Week 2 Larry Morris July 12, 2016 PROJECT WEEK 2 2 Using the ROI data set: 1. For each of the 2 majors calculate the mean, median, minimum, maximum, range, and standard deviation for the columns 'Cost' and '30-Year ROI'. Cost Data Analysis for Business Major Column 1 Mean $ 188,633.00 Standard Error $ 11,292.91 Median $ 215,200.00 Mode #N/ Standard Deviation $ A 50,503.43 Sample Variance $ 2,550,596,343.16 Kurtosi $ 0.02 Skewnes $ (1.26 s Rang $ 142,870.00 s ) Minimu $ 87,030.00 e Maximu $ 229,900.00 m Su $ 3,772,640.00 m Count $ 20.00 m PROJECT WEEK 2 3 30 Year ROI Business Major Column 1 Mean $ 1,477,800.00 Standard Error $ 29,727.06 Median $ 1,441,500.00 Mode #N/ Standard Deviation $ A132,943.44 Sample Variance $ 17,673,957,894.74 Kurtosi $ 1.06 Skewnes $ 1.31 s Rang $ 465,000.00 s Minimu $ 1,321,000.00 e Maximu $ 1,786,000.00 m Su $ 29,556,000.00 m Count $ 20.00 m 30 Year ROI Engineering Major PROJECT WEEK 2 4 Cost Data Analysis for Engineering Major Comparing both cost analysis data sheets, engineering majors have greater values in 4 out of the 7 categories whereas business majors only have 3. It appears that it is more expensive to become an engineering major and it is to major in business. 2. By hand or with Excel, for each of the 2 majors calculate the probability that a college picked from the column for 'School Type' is 'Private'. Engineering Major P=11/20 P=0.55 or 55% Business Major P=16/20 P=0.80 or 80% The probability is greater for a Business Major that a college picked from the School Type column is private. 3. By hand or with Excel, for each of the 2 majors find the probability that a college with the 'School Type' 'Private' has a '30-Year ROI' between $1,500,000 and $1,800,000. PROJECT WEEK 2 5 Engineering Major P=20/20 = 1 or 100% Business Major P=6/20 = 0.30 or 30% Engineering Majors have a 100% change of collecting a 30 year return on investment between $1,500,000 and $1,800,000. For individuals seeking a 30 year return in this price range, becoming engineering major is a no brainer. Business majors have a 30% change of earning a 30 year ROI in same financial bracket as engineering majors. Though the cost is greater to major in engineering, the offset is an even greater ROI. Running Header: Week 7 Project 1 Week 7 Project Grantham University Larry Morris August 16, 2016 Running Header: Week 7 Project 2 For each of the two majors: 1. Draw the scatter diagram of Y = 'Annual % ROI' against X = 'Cost'. Solution: The scatter diagram of Y =\"Annual % ROI against X=Cost is as follows: Scatter Diagram 14.00% 12.00% 10.00% 8.00% Annual ROI Annual ROI 6.00% 4.00% 2.00% 0.00% $50,000.00 $100,000.00 $150,000.00 Cost(X) $200,000.00 $250,000.00 Running Header: Week 7 Project 3 2. Obtain b0 and b1 of the regression equation defined as y = b0 + b1X and the coefficient of determination (r2) from the Excel regression output. Solution: The regression output is as follows: From the above result we come up with b0=0.1268 and b1=-2E-07 The regression equation is ^y =-2E-07* X+0.1268 The coefficient of determination (r2) is 0.9515 Running Header: Week 7 Project 4 3. Draw the fitted regression line on the scatter diagram. Solution: The fitted regression line on the scatter diagram is as follows: Scatter Diagram 14.00% 12.00% 10.00% f(x) = - 0x + 0.13 R = 0.95 Annual ROI Linear (Annual ROI) Linear (Annual ROI) 8.00% Annula ROI 6.00% 4.00% 2.00% 0.00% $50,000.00 $100,000.00 $150,000.00 $200,000.00 $250,000.00 Cost (X) 4. Calculate the estimated 'Annual % ROI' when the 'Cost' (X) is $160,000. Solution: Estimated Annual % ROI when Cost (X) is $160,000 Annual % ROI=0.1268-2E-07*$160000=0.0148=1.48% Running Header: Week 7 Project 5 5. Test the hypothesis: H0: 1 = 0 Ha: 1 0 Solution: Null hypothesis H0: 1 = 0 Vs Ha: 1 0 ^ 1 The test statistics will be t test and test statistics is t= 1 ^ Under the null hypothesis t= 1 From the regression output above t corresponds to Cost (X) =-18.7849 and the corresponding P value is 2.83396E-13. Since the P value corresponding to t=-18.7849 is 2.83396E-13 which is less than 0.05 at 5% level of significance therefore we reject the null hypothesis that 1 = 0. 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 Solution: We have seen that the estimated regression equation is ^y =-2E-07* X+0.1268 and the coefficient of determination of the regression line is 0.9515 which means the regression model explains 95.15% variation of the total variation and model is the best model to predict future observation, we have also seen from hypothesis test that Cost (X) is significant to the model and from the scatter plot we have seen that there is a strong correlation between Cost (X) and Annual % ROI. Running Header: Week 7 Project 6 For \"Business Major\" Excel sheet: For each of the two majors: 1. Draw the scatter diagram of Y = 'Annual % ROI' against X = 'Cost'. Solution: The scatter diagram of Y =\"Annual % ROI against X=Cost is as follows: Scatter Diagrram 12.00% 10.00% 8.00% Annual ROI 6.00% Annual ROI 4.00% 2.00% 0.00% $50,000.00 $100,000.00 $150,000.00 $200,000.00 $250,000.00 Cost (X) 2. Obtain b0 and b1 of the regression equation defined as y = b0 + b1X and the coefficient of determination (r2) from the Excel regression output. Solution: The regression output is as follows: Running Header: Week 7 Project 7 From the above result we get b0=0.118 and b1=-2E-07 Hence the regression equation is ^y =-2E-07* X+0.118 The coefficient of determination (r2) is 0.941 3. Draw the fitted regression line on the scatter diagram. Solution: The fitted regression line on the scatter diagram is as follows: Running Header: Week 7 Project 8 Scatter Diagram 12.00% 10.00% 8.00% Annual ROI f(x) = - 0x + 0.12 R = 0.94 Annual ROI Linear (Annual ROI) 6.00% 4.00% 2.00% 0.00% $50,000.00 $100,000.00 $150,000.00 $200,000.00 $250,000.00 Cost (X) 4. Calculate the estimated 'Annual % ROI' when the 'Cost' (X) is $160,000. Estimated Annual % ROI when Cost (X) is $160,000 Annual % ROI=0.118-2E-07*$160000=0.006=0.6% 5. Test the hypothesis: H0: 1 = 0 Ha: 1 0 Solution: Null hypothesis H0: 1 = 0 Vs Ha: 1 0 ^ 1 The test statistics will be t test and test statistics is t= 1 Running Header: Week 7 Project 9 ^ Under the null hypothesis t= 1 From the regression output in the above we get t corresponding to Cost (X) =-16.9475 and the corresponding P value is 1.64456E-12. Since the P value corresponding to t=-16.9475 is 1.64456E-12which is less than 0.05 at 5% level of significance therefore we reject the null hypothesis that 1 = 0. 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 Solution: From the above result we have seen that the estimated regression equation is y =-2E-07* X+0.118 and the coefficient of determination of the regression line is 0.941. The regression model explains 94.1% variation of the total variation and model is the best model to predict future observation, we have also seen from hypothesis test that Cost (X) is significant to the model and from the scatter plot we have seen that there is a strong correlation between Cost (X) and Annual % ROI. School Type Private Private Private Public Private Public Private Private Private Private Private Private Private Private Private Public Public Private Private Private Claimed mean = Sample mean = Sample Size = Sample Sd = Test Statistic = Df = P-value = Conclusion: 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 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 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% $160,000.00 $188,632.00 20 50503.42902376 2.5353960937 19 0.0201738795 p-value < significance level of 0.05 thus reject the null hypothesis in conclusion that the mean 'Cost' for a college for Business Major is different than $160,000. clusion that 00. School Type Private Private Private Private Private Public Private Private Public Private Public Private Public Private Public Public Public Public Private Public Claimed mean = Sample mean = Sample Size = Sample Sd = Test Statistic = Df = P-value = Conclusion: 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% $160,000.00 $164,680.00 20 66385.12190639 0.3152754061 19 0.755989071 p-value > significance level of 0.05, this do not reject the null hypothesis in conclusion that the mean 'Cost' for a college for Engineering Major is not different than $160,000. othesis in conclusion that t than $160,000. 30 Year ROI Business Major $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 30 Year ROI Engineering Major $2,412,000.00 $2,064,000.00 $1,949,000.00 $1,947,000.00 $1,938,000.00 $1,937,000.00 $1,915,000.00 $1,878,000.00 $1,854,000.00 $1,794,000.00 $1,761,000.00 $1,752,000.00 $1,727,000.00 $1,716,000.00 $1,703,000.00 $1,694,000.00 $1,690,000.00 $1,685,000.00 $1,676,000.00 $1,668,000.00 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 Major 1477800 17673957894.7368 20 0 35 -7.2039 0.0000 1.3062 0.0000 1.6896 The test statistic is negative and the one tailed p-value is smaller than the significance level of 0.10 Thus the null hypothesis is rejected in conclusion that the average '30-Year ROI' for Business majors is less than for Engineering Majors. 30 Year ROI Engineering Major 1838000 32327578947.3684 20 maller than the significance level of 0.10 verage '30-Year ROI' for Business majors