Case Study Forecasting Attendance at SWU Football Games

Southwestern University (SWU), a large state college in Stephenville, Texas, 30 miles southwest of the Dallas/Fort Worth metroplex, enrolls close to 20,000 students. In a typical town–gown relationship, the school is a dominant force in the small city, with more students during fall and spring than permanent residents.

A longtime football powerhouse, SWU is a member of the Big Eleven conference and is usually in the top 20 in college football rankings. To bolster its chances of reaching the elusive and long-desired number-one ranking, in 2008 SWU hired the legendary Billy Bob Taylor as its head coach. Although the number-one ranking remained out of reach, attendance at the five Saturday home games each year increased. Prior to Taylor’s arrival, attendance generally averaged 25,000 to 29,000 per game. Season ticket sales bumped up by 10,000 just with the announcement of the new coach’s arrival. Stephenville and SWU were ready to move to the big time!

The immediate issue facing SWU, however, was not NCAA ranking. It was capacity. The existing SWU stadium, built in 1953, has seating for 54,000 fans. The following table indicates attendance at each game for the past 6 years.

One of Taylor’s demands upon joining SWU had been a stadium expansion, or possibly even a new stadium. With attendance increasing, SWU administrators began to face the issue head-on. Taylor had wanted dormitories solely for his athletes in the stadium as an additional feature of any expansion.

SWU’s president, Dr. Marty Starr, decided it was time for his vice president of development to forecast when the existing stadium would “max out.” He also sought a revenue projection, assuming an average ticket price of $20 in 2014 and a 5% increase each year in future prices.

Discussion Questions

1. Develop a forecasting model, justify its selection over other techniques, and project attendance through 2015.

2. What revenues are to be expected in 2014 and 2015?

3. Discuss the school’s options.

Southwestern University Football Game Attendance, 2008–2013

2008 2009 2010 GAME ATTENDEES OPPONENT ATTENDEES OPPONENT ATTENDEES OPPONENT aHomecoming games. bDuring the fourth week of each season, Stephenville hosted a hugely popular southwestern crafts festival. This event brought tens of thousands of tourists to the town, especially on weekends, and had an obvious negative impact on game attendance. Source: J. Heizer and B. Render, Operations Management, 11th ed., © 2014. Reprinted and electronically reprod

In the late 1990s, the euro depreciated 15 percent against the dollar. As a result, European:

A. exports rose, boosting the economy. B. imports rose, boosting the economy. C. exports declined, dragging down the economy. D. imports declined, dragging down the economy.

Why did so many countries in Sub-Saharan Africa experience economic stagnation in the 1980s and 1990s? Is there any evidence of recovery in the last decade? Illustrate your answer with reference to literature and data relating to one or more Sub-Saharan African economy.

The accompanying data table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Complete the questions below. LOADING... Click the icon to view the data table. Use the range rule of thumb to identify a range of values containing the usual numbers of girls in 10 births. The maximum usual value is 0.2. ​(Round to one decimal place as​ needed.)x P(x)

0 0.004

1 0.017

2 0.043

3 0.112

4 0.206

5 0.234

6 0.202

7 0.114

8 0.041

9 0.011

10 0.016

A 0.1 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender​ selection, the proportion of baby girls is less than 0.5. Assume that sample data consists of 78 girls in 169 ​births, so the sample statistic of six thirteenths results in a z score that is 1 standard deviation below 0. -What is the null hypothesis and alternative hypothesis -what is the value of alpha -what is the sampling distribution of the sample statistic? -Is the test two-tailed, left tailed or right tailed? -what is the value of the test statistic? -P-value? -What are the critical values? - What is the area of the critical region? How to solve this with TI-83?

Consider an experiment in which a random family is selected among all families with exactly two children of which one is known to be a girl.

a. Write out the sample space and state the probability that the selected family has two girls.

b. Now consider an experiment in which we select a family randomly among all families with exactly two children, of which one is known to be a girl born on Tuesday. Write out the entire sample space taking into account the gender of the children and the day of the week they were born on.

c. What is the probability that the selected family has two girls?

d. Are the variables “day of the week” and “gender of child” dependent or independent?

In answering the question(s), make sure to write down the following 7 steps.

Step 1: Establish null and alternate hypotheses State the null and alternative hypothesis (as a sentence and formula).

Step 2: Calculate the degrees of freedom

Step 3: Calculate t _critical using critical t – table

Step 4: Calculate the Sum of Square deviation (SS_D)

Step 5: Calculate t _obtained

Step 6: Specify the critical value and the obtained value on a t-distribution curve

Step 7: Decision and Conclusion Write a clear and concise conclusion.

A researcher is interested in whether gender predicts the type of costume people would wear to an upcoming party. He asks 6 guys and 6 girls: How likely would you be to wear a “Creepy Clown” costume to the upcoming Halloween party? (1 = very unlikely to 7 = very likely). The data are shown below.

Guys: 4 6 4 3 6 7

Girls: 2 5 4 1 2 3

1. Use alpha = .01 to see whether gender impacts willingness to wear a Creepy Clown costume. (Note: You need to write down all the 7 steps.)

2. Use alpha = .01 to see whether guys are more willing than girls to a Creepy Clown costume. (Note: You only need to write down the steps that are different from part (1).)

3. Use alpha = .05 to see whether guys are more willing than girls to a Creepy Clown costume. (Note: You only need to write down the steps that are different from part (1).)

Denition:
An orthogonal array OA(k, n) on n symbols is an n² x k array such that, in any two columns, each ordered pair of symbols occurs exactly once.
Prove that there exists an OA(k, n) if and only if there exist (k - 2) mutually orthogonal Latin squares of order n.

(combinatorics and design)

Brutus Auto is a thriving, independently owned and operated firm located in Westerville. It was founded in 1986 by “Brutus” Cooper. Brutus was born and raised in Westerville, OH. Brutus is well-known and trusted by the residents of the town. As a teenager, he was a star football player for the high school team. In his spare time, he enjoyed working on cars and had a special talent when it came to cars. After college, this hobby led Brutus to start his own business – Brutus Auto Tire and Lube.

Brutus does a wide variety of work on vehicles of all makes and models. The shop also offers a variety of parts and supplies at retail. Brutus spends a great deal of time conversing with customers, most of whom he has known his whole life. His reputation for honest and reliable work has earned him many repeat customers, with the positive word of mouth helping him to expand his business.

His wife, Diane, runs the office, and takes special care to acknowledge customers on their birthdays with hand-written cards that include coupons for discounted services. Customers often reflect that Brutus offers the kind of service you can only find from a small-town mechanic. While Brutus is slightly more expensive than the chain establishments that have recently moved into town, customers testify that the friendly environment and quality service are worth the price.

Operational details

Brutus’s shop has grown steadily over the years. Originally, Brutus maintained a modest three automobile bays at his shop, and he and his long-time buddy, Fred, conducted most of the work except oil changes which were handled by a part-time apprentice. Currently, Brutus shop has six bays (the layout of the shop is shown in Figure 1) and seven mechanics (as not all of the service activities require a bay). Each of the bays is identical so that any employee can work at any station.

Four of the employees (including Brutus and Fred) are full-time (work at least 40 hours per week), and three are interns who work part-time (work fewer than 40 hours per week). Brutus and Fred are the only two mechanics permitted to do work beyond the basics, and so more involved car services can take some time getting through the shop. Most mechanics at Brutus Auto were trained at the area vocational school, and those with particular skill are taken on as apprentices who work under Fred and Brutus on the more involved projects. Cooper provides all the tooling necessary, and is respected as a fair and caring boss. In return, Brutus’ employees are loyal and hard-workers; seldom is absenteeism a problem, and turnover is rare.

The employee schedule for a typical week is shown in Table 1. The numbers shown in Table 1 are all devoted to working on vehicles. The shop closes for one week in the winter.

Inventory

Although the shop is primarily a service provider, all of the services require materials in addition to labor, and so there are inventory considerations that Brutus must manage.

A variety of other parts and supplies (for example, oil filters and oil) must be kept available due to the regularity of use; it would be difficult to meet the high expectations of customers if these items are not available. This has become a particularly high priority ever since national service chains moved into town, as the speed of their services such as oil changes is already far superior to that of Brutus. As a result of these competitive pressures, Brutus sets a 98% target service level.

Brutus is dedicated to using a high-quality brand of parts and supplies, most of which are available from a single supplier. Note that these parts and supplies are not only used to support services but also sold as retail transactions to customers who wish to perform their own repair work.

Currently, a continuous review policy is used for all car parts and supplies, but Brutus believes this system may require too much time to maintain for all inventory items. A sample of some of the items offered, the volumes used in services and sold at retail, and the associated costs are shown in Table 2. Brutus has determined that to call the supplier, pay for transportation, and put a shipment away costs approximately $50. The stockroom is relatively small and does not require special equipment or personnel. There is virtually no theft of product, so the annual holding costs are approximately 25% of unit cost. Delivery of orders takes about one week from the local supplier.

Adding Tire Service

The owners believe that adding tire replacement would increase revenues with a negligible increase to fixed (facility) costs other than tire inventory. However, in order to be competitive with the discount chains, Brutus must target a maximum of 30 minutes total time for each customer visit specific to tires since pricing was already competitive. They estimate that the time between arrivals for cars needing such replacement would be ten minutes. A dedicated and secure parking lot with a limit of 6 spots is available specifically for cars awaiting tire service. While service requirements vary, they estimate that a dedicated technician should finish up 3 tire service jobs each hour.

1. - Identify and describe TWO recommendations you would make to

                           Brutus Cooper to improve Operations and/or to lower costs.