The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x = 1.30 A, with a sample standard deviation of s = 0.42 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)

1. What are we testing in this problem? single mean or single proportion?

(a) What is the level of significance?

2. State the null and alternate hypotheses.

H₀: μ = 0.8; H₁:  μ > 0.8H₀: μ = 0.8; H₁:  μ ≠ 0.8     H₀: μ ≠ 0.8; H₁:  μ = 0.8H₀: p = 0.8; H₁:  p > 0.8H₀: p = 0.8; H₁:  p ≠ 0.8H₀: p ≠ 0.8; H₁:  p = 0.8

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t, since we assume that x has a normal distribution with unknown σ.The standard normal, since we assume that x has a normal distribution with known σ.     The standard normal, since we assume that x has a normal distribution with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Find (or estimate) the P-value.

P-value > 0.2500.125 < P-value < 0.250     0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.     At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the toy company claim of 0.8 A is too low.There is insufficient evidence at the 0.01 level to conclude that the toy company claim of 0.8 A is too low.    

Kim Hotels is interested in developing a new hotel in Seoul. The company estimates that the hotel would require an initial investment of $25 million. Kim expects the hotel will produce positive cash flows of $4 million a year at the end of each of the next 20 years. The project's cost of capital is 14%.

1. What is the project's net present value? Do not round intermediate calculations. Enter your answer in millions. For example, an answer of $1.23 million should be entered as 1.23, not 1,230,000. Round your answer to two decimal places.

   $    million

2. Kim expects the cash flows to be $4 million a year, but it recognizes that the cash flows could actually be much higher or lower, depending on whether the Korean government imposes a large hotel tax. One year from now, Kim will know whether the tax will be imposed. There is a 50% chance that the tax will be imposed, in which case the yearly cash flows will be only $2.9 million. At the same time, there is a 50% chance that the tax will not be imposed, in which case the yearly cash flows will be $5.1 million. Kim is deciding whether to proceed with the hotel today or to wait a year to find out whether the tax will be imposed. If Kim waits a year, the initial investment will remain at $25 million. Assume that all cash flows are discounted at 14%. Use decision-tree analysis to determine whether Kim should proceed with the project today or wait a year before deciding.

Marilyn Helm Retailers is attempting to decide on a location for a new retail outlet. At the​ moment, the firm has three​ alternatives: stay where it is but enlarge the​ facility; locate along the main street in nearby

Newbury​;

or locate in a new shopping mall in

Hyde Park.

The company has selected the four factors listed in the following table as the basis for evaluation and has assigned weights as​ shown:

​a) Based on the given​ information, the best location for Marilyn Helm Retailers is to open the new retail outlet in

Hyde Park

​, with a total weighted score of

54.5054.50.

​(Enter your response rounded to two decimal​ places.)

​b) A new subway station is scheduled to open across the street from the present location in about a​ month, so its third factor score should be raised to

40.

​Then, the best location for Marilyn Helm Retailers is to open the new retail outlet in

Hyde Park

Hyde Park

Newbury

Present Location

​, with a total weighted score of

nothing.

​(Enter your response rounded to two decimal​ places.)

Kim Hotels is interested in developing a new hotel in Seoul. The company estimates that the hotel would require an initial investment of $20 million. Kim expects that the hotel will produce positive cash flows of $3 million a year at the end of each of the next 20 years. The project's cost of capital is 13%. While Kim expects the cash flows to be $3 million a year, it recognizes that the cash flows could, in fact, be much higher or lower, depending on whether the Korean government imposes a large hotel tax. One year from now, Kim will know whether the tax will be imposed. There is a 50% chance that the tax will be imposed, in which case the yearly cash flows will be only $2.2 million. At the same time, there is a 50% chance that the tax will not be imposed, in which case the yearly cash flows will be $3.8 million. Kim is deciding whether to proceed with the hotel today or to wait 1 year to find out whether the tax will be imposed. If Kim waits a year, the initial investment will remain at $20 million. Assume that all cash flows are discounted at 13%. Use the Black-Scholes model to estimate the value of the option. Assume the variance of the project's rate of return is 7.32% and the risk-free rate is 6%. Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Do not round intermediate calculations. Round your answer to two decimal places.

Anil is planning a birthday party at an amusement park for his younger daughter and her friends. The manager of the park is considering whether to use uniform pricing or two-part-pricing. Anil's willingness to pay for rides for the party is p = 25 - 0.5Q, where p is the ticket price per ride and Q is the number of rides. The amusement park has a marginal cost of $5 for each additional ride. Its fixed cost for handling the party is $20.

a. Create a spreadsheet with quantity, price, consumer surplus, revenue, marginal revenue, cost, marginal cost, and profit as column headings. Fill in the spreadsheets cells for Q = 5 to Q = 50 in increments of 5 units. If the manager uses uniform pricing, what is the profit maximizing ticket price per ride, the number of rides, and the profit earned by the park?

b. Suppose that the manager uses two-part pricing: an entry fee for the entire party of young girls and price per ride. Calculate the profit-maximizing entry fee if the price per ride is the same as the monopoly price that you determined in part a. Calculate the total profit earned by the park.

c. Now suppose the manager uses two-part-pricing with a per-ride price equal to marginal cost and a profit-maximizing entry fee. Determine the price per ride, the number of rides, and the total profit (including profit from ticket sales and the entry fee) in this case.

Michael Wilson entered into a new business, hotel ownership, by buying a small 24 room hotel and café. The hotel is located in a remote area of Minnesota that is popular for tourists. Michael has hired you for advice.

Michael hired a young couple to run the hotel and café on a daily basis and plans to pay them a monthly salary. They will live for free in a small apartment adjacent to the office. The couple will be responsible for hiring and supervising five part-time personnel who will help with cleaning the rooms, cooking, waiting on customers in the café. The couple will maintain records of rooms rented, meals served, and payments received. They will also make weekly deposits.

Mike is concerned about his lack of control over the records and operations. Mike lives 5 hours away and will only be able to make periodic visits. Mike trusts the couple but wonders if it makes sense to place so much trust in employees.

Mike needs your help to identify possible ways that his motel and café could be defrauded and especially wants assistance to devise creative internal controls to help prevent or detect fraud.

Required

1. What are your two biggest concerns related to possible fraud for the hotel part of the business.   For each concern describe two controls that could reduce the risk.
2. What are your two biggest concerns related to the café part of the business. For each concern describe to controls to reduce risk.

1. Suppose that there are only three people that live in a (very) small town: Eric, Greg, and Katie. The town is thinking of building a park which you can assume is a public good for these three individuals in the town. Based on the individuals’ demand schedules for the park, which are given below, calculate and graph the social marginal benefit curve for the park.

b. Assume that the supply curve for the park is shown in the following chart. Graph this supply curve on your graph from part b. What is the socially optimal size of the park (in acres)?

Devos Inc. is building a hotel. It will have 4 kinds of rooms: suites where customers can smoke, suites that are non-smoking, budget rooms where the customers can smoke, and budget rooms that are non-smoking. When we build the hotel, we need to plan for how many rooms of each type we should have. The following are requirements for the hotel:

1. We want to figure out how many rooms of each type to build based on maximizing revenue if we fill up the hotel. We expect to charge $190 for a suite that is non-smoking and $140 for a budget room that is non-smoking. Smoking room customers for both suites and budget rooms will have to pay an additional $20 per night.
2. We can spend up to $7,500,000 on construction of our hotel. The cost to build a non-smoking budget room is $12,000. The cost to build a non-smoking suite is $15,000. It is $3,000 additional for a smoking room of either type for smoke detectors and sprinklers.
3. We require that the number of budget rooms be at least 1.5 times the number of suites, but no more than 3 the number of suites.
4. There needs to be at least 80 suites, but no more than 200.
5. Industry trends recommend that smoking rooms should be less than 50% of the non-smoking room and in addition, we require our builder gives us at least 4 smoking rooms.

The accompanying table, MultiLinear Regression 5, provides data for tar, nicotine, and carbon monoxide (CO) contents in a certain brand of cigarette. All measurements are in milligrams (mg).

MultiLinear Regression 5

Part a) Run the Multilinear Regression Analysis in Excel with both predictor variables. What is the adjusted R² value to the nearest hundredth of a percent (i.e. 45.67%)?
Adjusted R² =

Part b) What is the p-value for the full model? Round answer to nearest thousandth of a percent (i.e. 0.123%).
Model p-value =

Part c) What are the p-values for the variable coefficients? Round answers to the nearest hundredth of a percent (i.e. 0.12%)
Tar p-value =

CO p-value =

Part d) Run simple linear regression for just Nicotine & Tar and then for just Nicotine & CO. Write down the R²
values and p-values for those two models.

Part e) Using your analyses from parts a) through d), determine the model that is the best fit for these data. Use a significance level of 0.05, and consider each model’s p-value, R² value (or adjusted R² value), the p-values for each of the coefficients to determine the best fit model. Use that model to estimate the Nicotine level in a cigarette having 9 mg of tar and 9 mg of CO. Round answer to nearest hundredth of a milligram (i.e. 0.81 mg).
Predicted Nicotine Level =