Project_OPRE506Su23

xlsx

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University of Baltimore *

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506

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Statistics

Date

Jan 9, 2024

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xlsx

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103

Uploaded by BarristerRoseFalcon39

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You must show all of your work . You are w question(s) each Excel file you submitted are intended to an You are required to conduct all statistical analyses usin Handwritten work will not be accepted. All your statistical analyses must b result in a grade of zero. For each question that requires a statistical analysis, I must see at least on Your filled-out Excel templates ("Normal", "CIE Mean with Sigma Unknown Your Data Analysis ToolPak output ("t-Test: Paired Two Sample for Means" Your in-cell typed formulas (I must see the formula that starts with the “=” accepted.
welcome to submit multiple Excel workbooks (Excel files) as l nswer. ng Excel, in compliance with the section "Your Statistical Ana be completed using Excel. Any statistical analyses submitted that do not adh ne of the following: n", "Mean Z-test", ...) Those templates will be provided to you. ", "Regression", ...) ” sign when I click on your cell.) Using your Excel cells are a “textbox” will no
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long as you label them clearly, so I know what alyses" in your syllabus. here to the criteria I outline below will not be accepted and will ot be accepted. Any manual/by hand calculations will not be
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You are the CEO of a dairy company. You are planning to ex A random sample of 50 farms owned by your company is co number of laborers. The data can be found in the Excel Worksheet "MilkProdu
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xpand milk production by purchasing additional cows, lands a ollected on total milk production (in liters), the number of m uctionData".
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and hiring more workers. milking cows, land size (in acres) and the
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MILK COWS LAND LABOR 84729 18 24 4 101969 24 22.5 4 103314 22 32 4 70574 19 12.5 2 76144 21 31 2 86695 19 31.75 2 87600 22 31.75 2 105272 19 14.75 2 120422 24 15 2 68749 18 37.75 2 85541 20 37.75 2 91910 25 37.75 2 110465 26 37.75 2 125369 27 37.75 2 159470 29 37.75 2 102930 24 22.5 3 113214 25 26.25 3 133328 28 20 3 140086 26 32.5 3 145514 28 31 3 152589 27 20 3 128304 21 22.5 3 138093 24 28.5 3 161368 27 28.5 3 208136 33 27 3 224205 32 53.75 3 231090 32 32.25 3 122204 22 22.5 4 132311 25 24 4 155154 26 25.5 4 177268 29 24 4 196449 29 51.25 4 205324 28 89 4 89562 25 17.5 3 94840 21 17.25 3 94997 23 20 3 97625 24 25.25 3 102226 28 17.5 3 103832 25 17.5 3 239673 39 62.5 3 239861 40 62.5 3 241298 40 39.5 3 249196 39 62.5 3 294455 42 72.5 3 318871 47 72.5 3 66483 19 17.5 3
100459 20 20 3 103847 21 20 3 154141 25 20 3 155516 31 37.5 3
MILK Small Land Medium Land Large Land Two Labors 70574 76144 91910 105272 86695 110465 120422 87600 125369 Three Labors 102930 113214 145514 133328 138093 224205 152589 161368 231090 Four Labors 84729 132311 103314 101969 155154 196449 122204 177268 205324
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Q1. Estimating the mean land size for all farms: a. What is the probability that a random sample of 50 farm Your answer to Q1.a.: Please provide your answer, showin b. What is the probability that a random sample of 50 farm Your answer to Q1.b.: Please provide your answer, showin c. If you select a random sample of 50 farms, what will be t of the sample means? Your answer to Q1.c.: Please provide your answer, showin
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ms will have a mean land size that is above 28 acres? ng your work in Excel, in either a new Excel worksheet or a ms will have a mean land size that is below 30 acres? ng your work in Excel, in either a new Excel worksheet or a the lower limit and upper limit of the interval symmetrically ng your work in Excel, in either a new Excel worksheet or a s
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separate Excel workbook with a title of your choosing. separate Excel workbook with a title of your choosing. distributed around the population mean of land sizes that in separate Excel workbook with a title of your choosing.
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ncludes 80%
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Normal Probabilities Common Data Mean 32.5 Standard Error (Standard Deviation div 2.39 Probability for X > X Value 28 Z Value -1.8828452 P(X>28) 97% 97% Answer to 1a
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Q1. Estimating the mean land size for all farms: a. What is the probability that a random sample of 50 farms will have a mean land size that is above 28 acres? The probablity that a random sample of 50 farms will have a mean land size that is above 28 acres is 97%.
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Normal Probabilities Common Data Mean 32.5 Standard E 2.39 Probability for X <= X Value 30 Z Value -1.04602510460251 P(X<=30) 15% 15% Q1. b. W that The belo
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Estimating the mean land size for all farms: What is the probability that a random sample of 50 farms will have a mean land size t is below 30 acres? probablity that a random sample of 50 farms will have a mean land size that is ow 30 acres is 15%.
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Confidence Estimate for the Mean [Population Standard Deviation (Sigma) is Known] Data Population 61240.42 Sample Me 141853.44 Sample Siz 50 Confidence 80% Intermediate Calculations Standard E 8660.70325294245 Z Value -1.2816 Interval Ha 11099.1378 Confidence Interval a. Interval Lo 130754.3022 1307.54 Interval Up 152952.5778 1529.52
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Q1. Estimating the mean land size for all farms: c. If you select a random sample of 50 farms, what will be the lower limit and upper limit of the interval symmetrically distributed around the population mean of land sizes that includes 80% of the sample means? Please see table to the left.
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Q2. Estimating the mean milk production for all farms: a. Construct the 95% confidence interval estimate for the m Your answer to Q2.a.: Please provide your answer, showin b. Test a claim at 5% significance level that the true mean m Your answer to Q2.b.: Please provide your answer, showin
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mean milk production for all farms and provide your interpre ng your work in Excel, in either a new Excel worksheet or a milk production is at least 120K. ng your work in Excel, in either a new Excel worksheet or a
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etation. separate Excel workbook with a title of your choosing. separate Excel workbook with a title of your choosing.
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Confidence Estimate for the Mean [Population Standard Deviation (Sigma) is Unknown] Data Sample Standard Deviat 61240.42 Sample Mean 141853.44 Sample Size 50 Confidence Level 95% Intermediate Calculations Standard Error of the M 8660.7033 Degrees of Freedom 49 2.0096 Interval Half Width 17404.3348 Confidence Interval Interval Lower Limit 124449.11 Q2.A Interval Upper Limit 159257.77 t Value
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Q2. Estimating the mean milk production for all farms: a. Construct the 95% confidence interval estimate for the mean milk production for all farms and provide your interpretation. Please see table to the left of the textbox.
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t Test for the Hypothesis of the Mean Data 120000 Level of Si 0.05 Sample Siz 50 Sample Me 141853.44 Sample Sta 61240.42 Intermediate Calculations One-Tail Calculations Standard E 8660.7033 T.DIST.RT v 0.00746 Degrees of 49 1-T.DIST.RT 0.99254 2.5233 Two-Tail Test Lower Criti -2.0096 Upper Criti 2.0096 0.0149 Reject the null hypothesis Lower-Tail Test Lower Criti -1.6766 0.9925 Do not reject the null hypothesis Upper-Tail Test Upper Criti 1.6766 0.0075 Answer to Q2B Reject the null hypothesis Null Hypot t Test Statis p -Value p -Value p -Value Q2. Estimating th Test a claim at 5% Null Hypothesis ( H0: μ < 120k Alternative Hypo H1: μ ≥ 120k According to the that the mean tru than or equal to 1 The p-value is les least 120k.
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he mean milk production for all farms: % significance level that the true mean milk production is at least 120K. (H0) : The mean milk production is <120k liters. thesis (H1): The mean milk production is ≥ 120k liters. one-sample z-test, the null hypothesis is rejected and it is concluded that there is evidence ue milk production (M=141853.44, σ=61240.42) of the large quantities of pizza is greater 120k. (z=8, p<.05) ss than the significance level, therefore we can conclude that the mean milk production is at
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Q3. Studying the impact of land size and labor number on Among the existing farms, 27 farms were randomly selecte factors and their interactions on the milk production. ( Hint a. In the scenario above, why would you conduct an ANOVA Your answer to Q3.a.: b. Display your Excel ANOVA table. Your answer to Q3.b.: Please provide your answer, showin c. What are your statistical conclusions? Please justify. Your answer to Q3.c.: Please provide your answer, showin
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n milk production: ed with different levels of land size and labor number as show t: Use the table in the "MilkProductionData" Excel sheet, bet VA instead of t-test? ng your work in Excel, in either a new Excel worksheet or a ng your work in Excel, in either a new Excel worksheet or a s
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wn in Excel. Use ANOVA to indicate the importance of each o tween cells K9 and N18.) separate Excel workbook with a title of your choosing. separate Excel workbook with a title of your choosing.
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of the two
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Q3. Studying the impact of land size and labor number on milk production: Among the existing farms, 27 farms were randomly selected with different levels of land size and labo Excel. Use ANOVA to indicate the importance of each of the two factors and their interactions on the Use the table in the "MilkProductionData" Excel sheet, between cells K9 and N18.) a. In the scenario above, why would you conduct an ANOVA instead of t-test? We would conduct an ANOVA rather than a t-test because t-tests are typically used to compare the This scenario contains more than two. ANOVA also provides the ability to analyze two factors, wher only analyze a single factor. ANOVA can also examine the interaction between factors, whereas the doing so.
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or number as shown in milk production. ( Hint: e means of two groups. reas the t-test can e t-test is incapable of
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Anova: Two-Factor With Replication SUMMARYSmall LandMedium LaLarge LandTotal Two Labors Count 3 3 3 9 Sum 296268 250439 327744 874451 Average 98756 83479.67 109248 97161.22 Variance 6.53E+08 40563760 2.81E+08 3.7E+08 hree Labors Count 3 3 3 9 Sum 388847 412675 600809 1402331 Average 129615.7 137558.3 200269.7 155814.6 Variance 6.27E+08 5.8E+08 2.26E+09 1.99E+09 Four Labors Count 3 3 3 9 Sum 308902 464733 505087 1278722 Average 102967.3 154911 168362.3 142080.2 Variance 3.52E+08 5.05E+08 3.19E+09 1.91E+09 Total Count 9 9 9 Sum 994017 1127847 1433640 Average 110446.3 125316.3 159293.3 Variance 6.18E+08 1.32E+09 3.03E+09 ANOVA rce of Varia SS df MS F P-value F crit Sample 1.69E+10 2 8.47E+09 8.976339 0.001976 3.554557 Columns 1.13E+10 2 5.64E+09 5.979788 0.010201 3.554557 Interaction 5.87E+09 4 1.47E+09 1.554218 0.229233 2.927744 Within 1.7E+10 18 9.44E+08 Total 5.11E+10 26 Level Of significance 0.05 MILK Small LandMedium LaLarge Land Two Labor 70574 76144 91910 105272 86695 110465 120422 87600 125369 Three Labo 102930 113214 145514 133328 138093 224205 152589 161368 231090 Q3 b. D c. W Lab num H0: The of l H1: Acc of a Lan The H0: The lan H1: Acc ma Inte Acc evi mil (F=
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Four Labor 84729 132311 103314 101969 155154 196449 122204 177268 205324
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3. Studying the impact of land size and labor number on milk production: Display your Excel ANOVA table. Please see table to the left of the textbox. What are your statistical conclusions? Please justify. borers: The null hypothesis (H0): There is no evidence of a main effect on the mean milk production due to mber of laborers. : μ2Laborers = μ3Laborers = μ4Laborers e alternative hypothesis (H1): There is evidence of a main effect on the mean milk production due to the nu laborers. : μ2Laborers ≠ μ3Laborers ≠ μ4Laborers cording to the two-way ANOVA analysis we fail to reject the null hypothesis and conclude that there is evid a main effect on the mean milk production due to the number of laborers. (F=8.98, p<.05) nd size: e null hypothesis (H0): There is no evidence of a main effect on the mean milk production due to the land s : μSmall Land = μMedium Land= μLarge Land e alternative hyptothesis (H1): There is no evidence of a main effect on the mean milk production due to th nd size. : μSmall Land ≠ μMedium Land ≠ Large Land cording to the two-way ANOVA analysis we reject the null hypothesis and conclude that there is evidence o ain effect on the mean milk production due to the land size. (F=5.98, p<.05) eraction: cording to the two-way ANOVA analysis we fail to reject the null hypothesis and conclude that there is no idence of an interaction effect between the number of laborers and land size on the main effect on the mea lk production. =1.55, p>.05)
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the umber dence size. he of a an
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Q4. Investigate the relationships between all the variable You believe that the number of cows, land size and the num to test your assumptions, and provide your interpretations a. State your hypotheses. Your answer to Q4.a.: b. Display your Excel output for the multiple regression ana Your answer to Q4.b.: c. Write down the coefficient of determination and interpr Your answer to Q4.c.: d. Write down the regression equation and interpret all the Your answer to Q4.d.: Please provide your answer, showin e. What is the predicted milk production for a 30-acre farm Your answer to Q4.e.: Please provide your answer, showin
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es: mber of laborers are the best predictors for total milk produc s. alysis. ret its meaning. e coefficients. ng your work in Excel, in either a new Excel worksheet or a m with 20 milking cows and 3 labors? ng your work in Excel, in either a new Excel worksheet or a
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ction on any given farm. Perform a multiple regression analy separate Excel workbook with a title of your choosing. separate Excel workbook with a title of your choosing.
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ysis in Excel
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SUMMARY OUTPUT Regression Statistics Multiple R 0.949448 R Square 0.901452 Adjusted R 0.895025 89.50% Standard E 19841.84 Observatio 50 ANOVA df SS MS F ignificance F Regression 3 1.66E+11 5.52E+10 140.2586 3.738E-23 Residual 46 1.81E+10 3.94E+08 Total 49 1.84E+11 Coefficients tandard Erro t Stat P-value Lower 95%Upper 95% Lower 95.0% Upper 95.0% Intercept -105772 16389.11 -6.45381 6.029E-08 -138762 -72782.63 -138762 -72782.63 COWS 7271.581 596.6591 12.18716 5.259E-16 6070.568 8472.593 6070.568 8472.593 LAND 633.4088 233.1415 2.716843 0.009257 164.1193 1102.698 164.1193 1102.698 LABOR 11533.96 4405.487 2.618089 0.011931 2666.17 20401.74 2666.17 20401.74 Q4. In You be on any interp a. Stat Null H not th Altern can pr Accord eviden labore b. Disp c. Wri 89.50% d. Wri Y^=B0 X1=Nu X2=La X3=Nu B0 is - satisfa labore B1 is . increa B2 is 6 result B3 is 1 increa e. Wha Y^=B0 B0= -1 B1=72 B2=63 B3= 11 X1=20 X2=30
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X2=30 X3=3 Y^= 93
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nvestigate the relationships between all the variables: elieve that the number of cows, land size and the number of laborers are the best predictors for total milk pro y given farm. Perform a multiple regression analysis in Excel to test your assumptions, and provide your pretations. te your hypotheses. Hypothesis (H0): The number of cows, the extent of the land (in acres), and the number of laborers on a farm he greatest predictors of total milk production. native Hypothesis (H1): At least one of the variables (number of cows, quantity of land, and number of labo redict total milk production on a given property. ding to the Multiple Regression Analysis, we reject the null hypothesis and conclude that there is sufficient nce that at least one of the independent variables (the number of cows, the size of the land, and the numb ers) can predict total milk production. [3,46)= 140.26, p<.05] play your Excel output for the multiple regression analysis. Please see mulltiple regression to the left. ite down the coefficient of determination and interpret its meaning. % of the variability in total Milk production is explained by number of cows, land size, and number of labor ite down the regression equation and interpret all the coefficients. 0 + B1X1 + B2X2 + B3X3 umber of Cows and Size (Acres) umber of Laborers -105772.19. It is the Y-intercept, it is the value of Y when X is zero. In this example the product action is -105772.19 when the number of cows is 0, the Land size is 0 (in acres) and the number of ers is 0. There are no practical applications to this Y-intercept. .7271.58. As X1 grows by 1 unit, Y grows by B1. In this example, the total milk production (in liters ases by 7271.58 as the number of cows increases by 1. 633.41. As X2 grows by 1 unit, Y grows by B2 units. In this example, a one-unit increase in Land ar ts in a 633.41-liter increase in total milk production. 11533.96. As X3 grows by 1 unit, Y grows by B3. In this example, the total milk production (in liters ases by 11533.96 for each additional laborer. at is the predicted milk production for a 30-acre farm with 20 milking cows and 3 labors? 0+B1X1+B2X2+B3X3 105772.19 271.58 33.41 1533.9552 0 0
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0 3263.55
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oduction m are orers) t ber of rers. f s) rea s)
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ECQ. What is the relationship between one-sample test, tw Your answer to ECQ.: They are distinct assessments, but they all contain variabl conduct. A one-sample t-test is used when there is only on when there are more than or equal to two levels, the mea regression. In this test, you will determine how alterations
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wo-sample test, analysis of variance (ANOVA) and regression? les that can be compared. Based on the number of variable ne variable and you wish to compare the differences betwe ans of those levels are compared. There is one independen s to the independent variable will affect the dependent var
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? How do you decide on which test to perform? es to measure, you choose the appropriate test to een their means. In analysis of variance (ANOVA), nt variable and one dependent variable in riable.
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