5 applied statistics and probabilities case studies

Department of Industrial Engineering

( Dr. Abdulaziz Saud Alkabaa )FINAL PROJECT

INSTRUCTIONS:

Please SHOW ALL YOUR WORK ON SEPARATE PAGES FOR EACH

PROBLEM. Please submit your work on the blackboard, IN A ZIPPED FILE such as GROUP_1 CA_IE332_Final_Project_1_F20.zip.

Each team should answer all questions in each case study.

You are required to search for several resources such as websites, books, journals, questioning experts, etc., to get some information regarding your case study. References are required when you cite.

This project is a group work. In addition to your report, you are intended to present it, for 10 minutes, in the class using PowerPoint, Prezi, or other presentation software . (We may use BB ultra for this presentation)

Each question has its solution’s way that you should use (Software+ manually)

You can use α=0.05 if it is not mentioned in a question

( Page 2 of 6 )

Case studies

1. An experiment was conducted in order to evaluate the effectiveness of two devices for improving the efficiency of car engine systems. Engine efficacy was measured after one of the two devices was fixed. The two devices were an electric vent-200F (200F) and electric vent-149S (149S). The Engine efficacy data (BTU.In) are stacked in one column with a grouping column (Vent-type) containing identifiers or subscripts to denote the population. See attached excel file on tab (car_engine)

· Suppose that you performed a variance test and found no evidence for variances being unequal -Test the normality assumption (by graph and goodness of fit) and Show your work using confidence interval and hypothesis testing procedures to test the variances equality- (Solve manually and by Minitab + R studio)

· Now you want to compare the effectiveness of these two devices by determining whether or not there is any evidence that the difference between the devices is different from zero. - (Solve manually and by Minitab + R studio)

2. Suppose that you work at one of the largest grocery stores in Moscow. You have been involved in a quality control (QC) team to check a product’s specification that is related to wight from the same supplier, who supplies two supermarkets A and B. These products can be any fruit types such as apples, oranges, bananas, etc. Your duty is to visit any two supermarkets, that are from the same company, and measure each fruit’s weight from supermarket A and you do the same steps in supermarket B. You must select all products randomly and you have to list the steps that you follow for your selection. You may think about hypothesis testing and confidence interval to help your team in solving this problem. - (Solve manually and by Minitab + R studio)

3. In a shoe company want to compare two materials, A and B, for use on the soles of boys' shoes. In this problem, each of ten boys in a study wore a special pair of shoes with the sole of one shoe made from Material A in column (Mat-A) and the sole on the other shoe made from Material B in column (Mat-B). The sole types were randomly assigned to account for systematic differences in wear between the left and right foot. After three months, the shoes are measured for wear. See attached excel file on tab (shoe)

· Weight measurements were made on nine boys in column (weight lb). You know that the distribution of measurements has historically been close to normal with 

= 0.2. Test if the population mean is 50 and obtain a 90% confidence interval for the mean. - (Solve manually and by Minitab + R studio)

· You want to see if these is difference between the two materials. Justify your answers by using hypothesis testing and confidence interval procedures. - (Solve manually and by Minitab + R studio)

· Compare the results from the paired procedure with those from an unpaired- (Solve manually and Minitab)

4. You are hired by a ministry of health and you work as IE in the research and development (R&D) department. You are conducting a new research to analyze the number of COVID-19 in Moscow. You use a U chart to monitor the number of COVID-19 cases per month, however, a U chart assumes that data follow a Poisson distribution. Therefore, you as a professional IE, want to assess whether the number of COVID-19 cases follow a Poisson distribution. Records of the daily number of cases at this infection are available for 50 days. See attached excel file on tab (COVID-19)

How can you make sure that the number of COVID-19 cases follows a Poisson distribution? (Solve by Minitab)

5. Forecasting Ticket Revenue for A western Football Team Games

at Sport City

For a long time, a western football team set seat prices for its 15-game home schedule the same for each game. But when John, director of business strategy, finished his IE at the University, he developed a valuable database of ticket sales. Analysis of the data led him to build a forecasting model he hoped would increase ticket revenue. Studying individual sales of Western tickets on the open marketplace during the prior season, John determined the additional potential sales revenue the Western team could have made had they charged prices the fans had proven they were willing to pay on platform. This became his dependent variable, y , in a multiple-regression model.

The major factors he found to be statistically significant in determining how high the demand for a game ticket, and hence, its price, would be were:

· The temperature of the day ( x1 )

· Distance from where a team guest team come from ( x2 )

· The humidity of the day ( x3 )

Table 1 illustrates, for brevity in this case study, a sample

of 12 games that year (out of the total 15 home game regular season), including the potential extra revenue per game ( y ) to be expected using the variable pricing model.

A leader in football game variable pricing, the western team have learned that regression analysis is indeed a profitable forecasting tool.

Discussion Questions * (Solve using Minitab + R studio)

1. Use the data in Table 1 to build a regression model with three independent variables mentioned above.

2. Check the model adequacy

3. Which variables are significant? Justify your answer using ANOVA table

4. Use the data to build a model with the temperature of the day as the sole independent variable.

5. Using the multiple-regression model from question 1, what would be the additional sales potential of a 42 °C , 528.36 Km, and 79% ?

6. What additional independent variables might you suggest including in John’s model?

Table1. Data for Last Year’s Western Team Ticket Sales Pricing Model

Temp (°C)	Distance (KM)	Humidity%	Additional Sales Potential (S.R.)
43.36	1050.15	85.712	46,241.25
41.18	1108.37	68.006	108,765.00
37.27	899.25	25.359	410,295.00
42.53	52.36	49.301	284,208.75
43.15	1011.59	77.355	159,588.75
38.24	900.25	39.008	450,795.00
29.58	1086	21.286	76,721.25
34.11	3.15	38.987	866,325.00
37.45	795.25	45.665	106,706.25
43.49	75.25	84.933	414,603.75
39.22	958.25	32.674	168,641.25
32.14	952.88	27.638	113,463.75
30.27	1025.66	67.459	91,983.75
42.49	400.25	23.233	372,967.50
28.43	582.32	18.331	217,327.50

CONCLUSIONS AND DISCUSSION

Conclusion:

· Write about what you have learned from this project.

Best luck