1. The owner of Showtime Movie Theaters, Inc. would like to estimate weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

1. Develop an estimated regression equation in Excel with the amount of television advertising as the independent variable
2. Develop an estimated regression equation in Excel with both television advertising and newspaper advertising as the independent variables
3. Develop an estimated regression equation in Excel with all three independent variables: television advertising, newspaper advertising, and radio advertising
4. Is the estimated regression equation coefficient for television advertising expenditures the same in par a), in part b) and in part c)? Interpret the coefficient in each case
5. Obtain and compare the multiple coefficient of determination and the adjusted multiple coefficient of determination for parts a), b) and c). How does the coefficient of determination changes as a result of adding more independent variables in the equation?
6. What is the estimate of the weekly gross revenue for a week when $3500 is spent on television advertising, $1800 is spent on newspaper advertising, and $350 in radio advertising?
7. Use the F test to determine the overall significance of the relationship. What is the conclusion at the .05 level of significance?
8. Use the t test to determine the significance of each independent variable. What is your conclusion at the .05 level of significance?
1. Determine the sample correlation coefficient between all possible pairs of independent variables to measure multicollinearity. Is there any value high enough to predict any potential problem in the regression model? Explain

SHOW ALL WORK

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below. Wilderness District 1 2 3 4 5 January 140 123 123 64 78 April 102 111 104 88 61 Does this information indicate that the peak wind gusts are higher in January than in April? Use α = 0.01. Solve the problem using the critical region method of testing. (Let d = January − April. Round your answers to three decimal places.) test statistic = critical value = Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. Reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. Fail to reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? We reject the null hypothesis using the critical region method, but fail to reject using the P-value method. The conclusions obtained by using both methods are the same. We reject the null hypothesis using the P-value method, but fail to reject using the critical region method.

DataSpan, Inc., automated its plant at the start of the current year and installed a flexible manufacturing system. The company is also evaluating its suppliers and moving toward Lean Production. Many adjustment problems have been encountered, including problems relating to performance measurement. After much study, the company has decided to use the performance measures below, and it has gathered data relating to these measures for the first four months of operations.

Management has asked for your help in computing throughput time, delivery cycle time, and MCE. The following average times have been logged over the last four months:

Required:

1-a. Compute the throughput time for each month. (Round your answers to 1 decimal place.)

1-b. Compute the manufacturing cycle efficiency (MCE) for each month. (Round your answers to 1 decimal place.)

1-c. Compute the delivery cycle time for each month. (Round your answers to 1 decimal place.)

3-a. Refer to the move time, process time, and so forth, given for month 4. Assume that in month 5 the move time, process time, and so forth, are the same as in month 4, except that through the use of Lean Production the company is able to completely eliminate the queue time during production. Compute the new throughput time and MCE. (Round your answers to 1 decimal place.)

3-b. Refer to the move time, process time, and so forth, given for month 4. Assume in month 6 that the move time, process time, and so forth, are again the same as in month 4, except that the company is able to completely eliminate both the queue time during production and the inspection time. Compute the new throughput time and MCE. (Round your answers to 1 decimal place.)

A plane goes missing. According to air trac control, the probability that it has gone
missing in region A is 0.2 and in region B is 0.6. From knowledge of these regions, it is
known that if a plane goes missing in region A, the probability that it will be found is 0.7,
while if a plane goes missing in region B, the probability of it being found is 0.6.
Using probability notation, answer the following questions.
(a) What is the probability that the plane did not go down in either region A or B? Justify
your answer.
(b) If the probability of the plane being found if it goes down outside regions A or B is
0.1, what is the total probability of the plane not being found at all?
(c) If the plane isn't found, what is the probability it went down in region A?
(d) If two planes go missing independently, what is the probability that they are both
found?

A plane goes missing. According to air trac control, the probability that it has gone
missing in region A is 0.2 and in region B is 0.6. From knowledge of these regions, it is
known that if a plane goes missing in region A, the probability that it will be found is 0.7,
while if a plane goes missing in region B, the probability of it being found is 0.6.
Using probability notation, answer the following questions.
(a) What is the probability that the plane did not go down in either region A or B? Justify
your answer.
(b) If the probability of the plane being found if it goes down outside regions A or B is
0.1, what is the total probability of the plane not being found at all?
(c) If the plane isn't found, what is the probability it went down in region A?
(d) If two planes go missing independently, what is the probability that they are both
found?

Question 3:

Use the annual flood data (annual maximum series) in the table below to perform a flood frequency analysis using the U.S. Water Resources Council Guidelines. The map skew for this location is - 0.2

Fill out the following table

Use the annual flood data (annual maximum series) in the table below to perform a flood frequency analysis using the U.S. Water Resources Council Guidelines. The map skew for this location is - 0.2

Fill out the following table

Since its opening in 1977, Ocean Park was the only theme park in Hong Kong. The park, owned by the Hong Kong government, is a nonprofit organization that aims to provide visitors a unique experience in entertainment, education, and conservation. In the absence of competition, Ocean Park had existed without direction and focus. When Hong Kong officials signed an agreement to bring Disneyland to Hong Kong in 1999, it seemed as if it would be the end of Ocean Park. In this unequal competition, Ocean Park emerged the surprise winner. Quickly sprucing up its act, it has managed to outperform Disneyland and has emerged as the number one amusement park in Hong Kong .

How was Ocean Park able to turn a threat into an opportunity?

Ocean park made the decision not to compete head to head with Disneyland. Will this strategy always work when local companies face multinational giants? Explain.

How can Ocean Park further capitalize on Disneyland’s presence? (hint: check out how other parks surrounding Disney, such as Sea World and Universal Studios, survive and thrive in

Anaheim, California, and Orlando, Florida.)

How can Hong Kong Disneyland turn around its lackluster performance?

QUESTION 3 (Modules 7-8) Woody Paints (WP) produces two paint types – the Silky and the Smooth. Projected sales (in units) for the 2 products in litres for 2019 - 2021:

                                                            2019              2020                  2021                  2022

Silky                                                  120,000          130,000            135,000           135,000

Smooth                                           70,000               80,000               85,000           85,000

Current sales prices in 2018 Silky $8 per litre & Smooth $10 per litre (expected to increase by 2% in 2019 and then remain stable for 3 years)

? Inventories are planned for each product so that projected ending finished goods inventory is 10% of the following year’s projected sales in units.

? The per unit raw material requirements for one litre of the products are as follows:

                                                                       Silky         Smooth        Cost per litre/kg

Base paint litres                                            0.8             0.7                     $0.50

Additives kilograms                                     0.1              0.2                      $2.00

Container (1 per unit)                                                                                  $0.20

The desired materials ending inventory is 50% of that required for the next year’s production.

Opening materials inventories:

Base paint               litres                                         72,500

Additives                kilograms                                 9,500

Containers             units                                           65,000

Direct Labour required per unit/litre (at $15 per hour – no increase expected)

                                                             Silky        Smooth

Labour hours                                       0.1           0.2

Opening finished goods inventories (in units):

Silky 60,000

Smooth 35,000

The desired ending finished goods inventory is equal to the 10% of following year’s sales in units

Required:

For the two years 2019 and 2020:

(note: use the excel templates provided)

a) Prepare a sales budget in units and dollars

b) Prepare a production budget in units for the Silky and the Smooth paint products.

c) Prepare direct materials usage budgets in units for each of the materials (separate budgets) and calculate the dollar purchases for each, showing the 2 years, for the Silky and the Smooth paint products. Note that as both products use the same materials, these materials budgets should be for the combined usage of the Silky and the Smooth paint e.g. total Base paint needed for both each year.

d) Calculate the total value of materials purchases each year. (1 mark)

e) Prepare a direct labour budget.

f) Actual production of Silky paints in 2019 turned out to be 75,000 units (litres), using 9,375 kg of additives at a cost of $16,875. Calculate the materials price and volume variance for the additives for Silky paints in 2019. (4 Marks

In a backyard vineyard in Napa Valley with 10 grape vines in a row, if the weather works well (just right), rain in the Spring and dry through summer, the yield for each vine is distributed roughly binomial with N=800, p=0.5. In a drought the yield is Binomial with N=800 and P=0.48, while if the year is too wet, the yield of useful grapes per vine is N=600, P=0.2. Under climate change the probability of just the right year is about 0.2 of a too wet year is 0.1, and a dry year is 0.7. On a just right year the wine can sell for 100 dollars/bottle, on a dry year the quality drops so it will sell for 60 dollars a bottle, on wet year it will sell for 30 dollars a bottle (For a Z score with absolute value >5 assume the probability is 0) The yield for all 10 vines was more than 3900 grapes. Given this yield:

a) What is the probability that you will be able to sell for 100 dollars a bottle?

b) What is the probability that you will be selling for 60 dollars a bottle?

c) What is the probability that you can only sell for 30 dollars a bottle?

d) What is your expected revenue per bottle?