## Question

1. Refer to the NFL data on Exhibit 1. Using StatCrunch, find the value of the correlation coefficient between the Points Scored per Game and the Points Allowed per Game. Check the box to find the two sided p-value you'll need for the next question. Report the correlation coefficient here and round your result to two decimal places.

Question 2

1. Refer to your results for the correlation calculation using Exhibit 1. Explain in non-statistical terms what the sign of the correlation coefficient indicates and then explain the implications of the p-value.

Question 3

1. Using the NFL data on the Exhibit 1 tab of the Final Exam Excel file, create a multiple regression model to predict the number of wins using the other variables in the table. Report your regression equation here and round answers to two decimal places. If your entry is negative, include the negative sign. Use a leading zero if the number is smaller than 1. Be careful to match up the coefficients and their variables in case your model is in a different order.

The expected number of wins is given by _______ + ________* Fum Lost + __________ * Points Scored/G + _________ * Points Allowed/G + _______* Time of Possession.

Question 4

1. Using the model you created for the NFL data on the Exhibit 1 tab, and rounding the coefficients to two decimal places, what number of wins does the model predict for the Indianapolis Colts at this point of the season? Round your answer to three decimal places.

Question 5

1. Refer to the multiple regression model you created for the NFL data on the Exhibit 1 tab. Discuss the implications of the statistical properties of this model (the F statistic, the t statistics, and the R squared value). and indicate whether or not there should be any revisions to this model.

Question 6

1. Refer to the Exhibit 2 tab in the Final Exam Excel file. Create a time series plot for this data. Discuss the presence/absence of trend and of seasonality. Be specific about whether the trend is nonexistent, linear, or nonlinear and how many, if any, seasons there are.

Question 7

1. A seasonal decomposition model for quarterly data has the trend equation

Trend = 91 + 7.07t

The seasonal indexes are 1.05 for Quarter 1, 0.92 for Quarter 2, 0.88 for Quarter 3, and 1.15 for Quarter 4. Time began with observation 1 in the the first quarter of year 1. Calculate the forecast for the third quarter of year 5.

Question 8

1. Evaluate the derivative of this function at x = 4

f(x) = 5x3+3x2-30x+-29x0.5+1,755

Question 9

1. Cost accountants have examined historical data and contracts and have determined that the marginal cost for producing one of the company's products is given by the formula

(X^2)-35x+250

Which of the following best describes the cost function?

Cost is minimized at x = 17.5 and maximized at x = 35. These are relative values.

Cost is minimized at x = 25 and maximized at x = 10. These are relative values.

Cost is maximized at x = 17.5 and minimized at x = 35. These are relative values.

Cost is maximized at x = 25 and minimized at x = 10. These are relative values

Question 10

1. Calculate the value of the definite integral of this function between x = 3 and x = 7

f(x) = 19x2-27x+0

Round your answer to two decimal places

Question 11

1. In an ordering decision, the cost for the store to purchase a unit from its supplier is 36. The store sells each unit for a price of 70. If the store runs out of inventory, it can special order more at a cost of 12 per unit above the original cost. Alternatively, if demand is smaller than supply, the store can sell the leftover units at half price to an inventory buyer.

What is the payoff if the store buys 50 units and demand is 60?

Question 12

1. Refer to the Exhibit 3 tab in the Final Exam Excel file. Use the payoff table you find there to answer the questions that follow.

The decision maker who chooses to follow the Maximax rule will choose decision Blank 1 and hope to receive Blank 2.

The decision maker who chooses to follow the Maximin rule will chooose decision Blank 3 and is guaranteed to receive at least Blank 4.

Question 13

1. Refer to the Exhibit 3 tab in the Final Exam Excel file. Create the regret table for this payoff table and determine the best course of action for the decision maker who follows the Minimax Regret rule.

This decision maker would choose alternative Blank 1. The worst this decision maker could feel is a regret of Blank 2.

Question 14

1. Refer to the table in Exhibit 3 and your work from the previous two questions. Which of the four alternatives would you choose, assuming the numbers represent dollars? Explain your reasoning. Would your answer change if the numbers represented thousands of dollars coming to you? There is no right or wrong answer to this question, but you do need to include a thoughtful explanation.

Question 15

1. When customers buy electronic equipment, they are often asked if they'd like to purchase an extended warranty. Consider at item that costs the customer $240. There are two uncertain outcomes in this situation--either the item breaks completely, in which case the store provides a full refund, or the item is perfect. The probability that the item will break completely is 0.09. What is the minimum value the store should charge for the warranty in order to cover its expected cost?

Question 16

1. This is a basic statistics review problem to check your understanding of hypothesis testing.

Industry average annual spending for a bank credit card is $6215. If the bank finds that its customers spend more than the average, it will take steps to more aggressively market use of its credit card. Use α = 0.05.

Hypothesis test results:

H0 : μ = 6215

HA : μ > 6215

Sample mean = $6378.20

p-value = 0.2348

Which is the best conclusion for this hypothesis test?

The sample mean is larger than $6215. The bank should market the card.

The evidence is strong enough to reject the null hypothesis. The bank should market the card

Question 17

1. Like many of their peers, Ben, Megan, and Anthony dreamed of starting their own business in their college town. Because the town closely follows all the college sports as well as the local high school and AAU games, the three decided to offer tailgate party packages under the name of BMA Tailgating. The customer orders one of the four packages and BMA prepares the food and delivers it to the customer’s location. For each of the scenarios that follows, match the most appropriate statistical tool.

Over several football seasons, the share of sales for the four packages are at 30%, 15%, 42%, and 13%. BMA wants to see if orders during the summer follow the same percentages.

BMA wonders if, during football season, the number of customers who place an order is related to the expected high temperature.

Megan is in charge of purchasing and has noticed a general increase in the cost of chicken. Before negotiating the next contract, she would like to predict the cost three months from now.

Anthony remembers learning about inventory cost in his operations management class and has developed a nonlinear cost function for the foil containers BMA uses to deliver all its food. He’d like to understand how many containers to buy at a time to reduce cost.

Ben has tallied the number of orders for each of the four packages during the summer season and the weather (wet or dry) for each day. Is there a relationship?

BMA’s packages use a lot of corn chips. Although monthly demand fluctuates somewhat, it is fairly steady and there doesn’t seem to be any pattern based on time of year. What kind of forecasting should they use?

Business has been good enough that the owners are considering buying a van to use in addition to their three cars. Should they buy new or used? If they buy used, should they buy an extended warranty?

In order to understand weekly demand during the summer season, the owners have collected data on the number of games that are scheduled, whether or not there is a tournament going on, and the number of orders during the same week the year before.

Decision Analysis

Question 15

1. When customers buy electronic equipment, they are often asked if they'd like to purchase an extended warranty. Consider at item that costs the customer $240. There are two uncertain outcomes in this situation--either the item breaks completely, in which case the store provides a full refund, or the item is perfect. The probability that the item will break completely is 0.09. What is the minimum value the store should charge for the warranty in order to cover its expected cost?

Question 16

1. This is a basic statistics review problem to check your understanding of hypothesis testing.

Industry average annual spending for a bank credit card is $6215. If the bank finds that its customers spend more than the average, it will take steps to more aggressively market use of its credit card. Use α = 0.05.

Hypothesis test results:

H0 : μ = 6215

HA : μ > 6215

Sample mean = $6378.20

p-value = 0.2348

Which is the best conclusion for this hypothesis test?

The sample mean is larger than $6215. The bank should market the card.

The evidence is strong enough to reject the null hypothesis. The bank should market the card

The evidence is strong enough to reject the null hypothesis. There is no need to market the card.

The evidence is not strong enough to reject the null hypothesis. The bank should market the card.

The evidence is not strong enough to reject the null hypothesis. There is no need to market the card.

Question 17

A. Correlation

B. Trend forecasting

C. Test of Independence

D. Test of Goodness of Fit

E. Optimization

F. Simple Exponential Smoothing

G. Multiple Regression

H. Decision Analysis

Like many of their peers, Ben, Megan, and Anthony dreamed of starting their own business in their college town. Because the town closely follows all the college sports as well as the local high school and AAU games, the three decided to offer tailgate party packages under the name of BMA Tailgating. The customer orders one of the four packages and BMA prepares the food and delivers it to the customer’s location. For each of the scenarios that follows, match the most appropriate statistical tool.

1. Over several football seasons, the share of sales for the four packages are at 30%, 15%, 42%, and 13%. BMA wants to see if orders during the summer follow the same percentages.

2. BMA wonders if, during football season, the number of customers who place an order is related to the expected high temperature.

3. Megan is in charge of purchasing and has noticed a general increase in the cost of chicken. Before negotiating the next contract, she would like to predict the cost three months from now.

4. Anthony remembers learning about inventory cost in his operations management class and has developed a nonlinear cost function for the foil containers BMA uses to deliver all its food. He’d like to understand how many containers to buy at a time to reduce cost.

5. Ben has tallied the number of orders for each of the four packages during the summer season and the weather (wet or dry) for each day. Is there a relationship?

6. BMA’s packages use a lot of corn chips. Although monthly demand fluctuates somewhat, it is fairly steady and there doesn’t seem to be any pattern based on time of year. What kind of forecasting should they use?

7. Business has been good enough that the owners are considering buying a van to use in addition to their three cars. Should they buy new or used? If they buy used, should they buy an extended warranty?

8. In order to understand weekly demand during the summer season, the owners have collected data on the number of games that are scheduled, whether or not there is a tournament going on, and the number of orders during the same week the year before.

## Solution Preview

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Question 11. Refer to the NFL data on Exhibit 1 of the Final Exam Excel file. Using StatCrunch, find the value of the correlation coefficient between the Points Scored per Game and the Points Allowed per Game. Check the box to find the two sided p-value you'll need for the next question. Report the correlation coefficient here and round your result to two decimal places.

The value of the correlation coefficient between the Points Scored per Game and the Points Allowed per Game is -0.13.

Question 2

1. Refer to your results for the correlation calculation using Exhibit 1. Explain in non-statistical terms what the sign of the correlation coefficient indicates and then explain the implications of the p-value.

We can see that the correlation coefficient in negative, it means that there is a negative relationship between these two variables. If one variable in increasing, the other is decreasing and vice-versa. The p-value is 0.487 which is bigger than 0.05, it means that this correlation is not statistically significant.

Question 3

1. Using the NFL data on the Exhibit 1 tab of the Final Exam Excel file, create a multiple regression model to predict the number of wins using the other variables in the table. Report your regression equation here and round answers to two decimal places. If your entry is negative, include the negative sign. Use a leading zero if the number is smaller than 1. Be careful to match up the coefficients and their variables in case your model is in a different order.

The expected number of wins is given by _______ + ________* Fum Lost + __________ * Points Scored/G + _________ * Points Allowed/G + _______* Time of Possession.

The expected number of wins is given by 4.92-0.22* Fum Lost + 0.31 * Points Scored/G -0.29* Points Allowed/G + 0.07* Time of Possession....

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