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The ABC Floral Shop sold the following number of geraniums during the last two weeks.

Day Demand Day Demand
1 200 8 154
2 134 9 182
3 147 10 197
4 165 11 132
5 183 12 163
6 125 13 157
7 146 14 169

The ABC Floral Shop is considering fitting various forecasting models on the first seven days of demand and using the second seven days as a hold-out sample for comparing the prediction accuracy of the models. They have decided to use a = 0.25, but aren’t sure what starting value of forecast, F1, to use.

(Round all answers to 1 decimal place.)

a. Try values of F1 = 160, 170,180 to determine the best exponential model for the first seven days using the minimum total absolute deviation as the criterion.

F1= 160

Day Demand (t) Forecast (t) Absolute Error (t)

1

 200 160.0
2 134
3 147
4 165
5 183
6 125
7 146
Total

F1 = 170

Day Demand(t) Forecast (t) Absolute Error (t)
1 200 170.0
2 134
3 147
4 165
5 183
6 125
7 146
Total

F1 = 180

Day Demand (t) Forecast(t) Absolute Error (t)
1 200 180.0
2 134
3 147
4 165
5 183
6 125
7 146
Total

Which of the above forecasts is the best?

multiple choice 1

  • Using 160.0

  • Using 170.0

  • Using 180.0

b. Compare the best model from part a to a three-period moving average model on the second set of data.

Day Demand (t) Forecast (t) Absolute Error (t)
8 154
9 182
10 197
11 132
12 163
13 157
14 169
Total

3-period moving average

Day Demand (t) Forecast (t) Absolute Error (t)
8 154
9 182
10 197
11 132
12 163
13 157
14 169
Total

Which one has the smallest sum of absolute errors?

multiple choice 2

  • 3-period moving average

  • Exponential Smoothing

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Davis v. Watson Brothers Plumbing, Inc.

FACTS Arnett Lee presented a $152.38 check for cashing to the plaintiff, liquor store operator Troy Davis. After Davis gave Lee the cash, Lee requested a bottle of scotch and a six-pack of beer. As Davis turned to fill the order, a thief stole $110.00 of the $152.38. Lee immediately contacted the defendant-drawer of the check, Watson Brothers Plumbing, Inc., and notified them of the loss. The defendant (Watson) then issued another check for $152.38 and stopped payment on the first check held by Davis. Davis brought this action against Watson for the full amount of the check.

DECISION Judgment for Davis for $152.38.

OPINION Davis was the holder of the check, and Watson failed to raise any valid defense to enforcement of the check against it. Any party “who is in possession of … an instrument … indorsed to him … in blank” is a “holder.” Since Lee indorsed the check in blank to Davis, Davis is a holder. The holder of a draft is entitled to receive its full amount from the drawer upon dishonor of the check, unless the drawer has a valid defense to the holder’s enforcement of the check against it. Watson argues that it may raise the defense of insufficiency or failure of consideration in the transaction between Davis and Lee. But the transfer of the check by Lee to Davis has no effect upon Watson’s obligation to pay the check according to its tenor. “Consideration” is concerned with Lee’s transaction with Watson, not with whether Davis gave anything in consideration for the check to Lee. Since Watson has no defense to enforcement of the check against Lee, it has no defense against Davis, regardless of whether Davis gave full consideration for the check.

INTERPRETATION The drawer’s liability is contingent upon dishonor of the instrument.

CRITICAL THINKING QUESTION Should the drawer be permitted to raise defenses of other parties to the instrument? Explain.

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According to the Office for National Statistics’, the average weekly wage of a professional is £704.1 a week and the average weekly wage of a manager and senior official is £721.7. Assume that such wages are normally distributed in the population and that the population variances are equal. Suppose these figures were actually obtained from the data below.

a. Use these data and  0.10 to test to determine if there is a signifi cant diff erence in the mean weekly wage of a professional and the mean weekly wage of manager and senior official.

b. Using these same data, construct a 90% confi dence interval to estimate the difference in the population mean weekly wages of professionals and managers and senior officials.

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Putting It Together: Weldon’s Dice On February 2, 1894, Frank Raphael Weldon wrote a letter to Francis Galton that included the results of 26,306 rolls of 12 dice. Weldon recorded the results such that a roll of a 5 or 6 resulted in a success, while a roll of 1, 2, 3, or 4 was a failure. The number of successes in each roll of the 12 dice is recorded in the table.

(a) What is the probability of rolling a 5 or 6 when throwing a six-sided fair die?

(b) Treating the probability determined in part (a) as the probability of success, compute the theoretical probability of 0, 1, 2, … , 12 successes in throwing 12 dice.

(c) Use the probabilities found in part (b) to determine the expected frequency in observing 0, 1, 2, … , 12 successes after throwing the 12 dice 26,306 times.

(d) Conduct a goodness-of-fit test to determine if the number of successes follows a binomial probability distribution. Note: Combine 11 and 12 into a single bin.

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