A magazine reported that at the top 50 business schools in a​ region, students studied an average of 17.8 hours. Set up a hypothesis test to try to prove that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark. Complete parts​ (a) through​ (c) below.

a. State the null and alternative hypotheses. Choose the correct answer below.

A. Upper H 0​: alpha not equals 17.8 Upper H 1​: alpha equals 17.8

B. Upper H 0​: beta not equals 17.8 Upper H 1​: beta equals 17.8

C. Upper H 0​: muequals17.8 Upper H 1​: Upper X overbarnot equals17.8

D. Upper H 0​: Upper X overbarequals17.8 Upper H 1​: Upper X overbarnot equals17.8

E. Upper H 0​: alpha equals 17.8 Upper H 1​: beta not equals 17.8

F. Upper H 0​: munot equals 17.8 Upper H 1​: Upper X overbar equals17.8

G. Upper H 0​: alphaequals17.8 Upper H 1​: alphanot equals17.8

H. Upper H 0​: muequals17.8 Upper H 1​: munot equals17.8

I. Upper H 0​: Upper X overbarnot equals17.8 Upper H 1​: Upper X overbarequals17.8

J. Upper H 0​: alphanot equals17.8 Upper H 1​: betaequals17.8

K. Upper H 0​: munot equals17.8 Upper H 1​: muequals17.8

L. Upper H 0​: betaequals17.8 Upper H 1​: betanot equals17.8

b. What is a Type I error for your​ test?

A. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is different

B. Concluding that the mean number of hours studied at your school is not different from the reported 17.8 hour benchmark when in fact it is different

C. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is not different

c. What is a Type II error for your​ test?

A. Concluding that the mean number of hours studied at your school is not different from the reported 17.8 hour benchmark when in fact it is different

B. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is different

C. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is not different

(1 point) A national sporting good store wishes to use demographic information to predict its monthly sales, in $1000s. Thrity-eight, n=38n=38, stores of the chain are randomly chosen across the country. It is known that each store is approximately the same size and carries the same merchandise.

The geographic area from which a store draws its customers is known as the customer base. One of the variables is the percentage of the customer base who have graduated from high school.

MonthlySalesiMonthlySalesi = β0β0 + β1PercentHSGradsiβ1PercentHSGradsi + eiei

where

MonthlySalesiMonthlySalesi - is the total sales in month ii, in $1000s

PercentHSGradsiPercentHSGradsi - is percentage of all customers in store ii customer base that have graduated from high school

A least-squares regression was ran in R producing the following output:



Regression Analysis: MonthlySales versus PercentHSGrads

S = 802.004 R-Sq =

Using the partial R output, answer the questions below.

(a) Estimate the model. Use two-decimals your estimation of the slope term, no decimals in the estimation of the y-intercept.


MonthlySalesiˆMonthlySalesi^ =

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+

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PercentHSGradsiPercentHSGradsi

(b) What percentage of the variation in a store's monthly sales cannot be explained by its linear dependency on the percentage of the customer base that are high school graduates? Enter your answer as a percentage, using two decimal places.

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%


(c) Does the data collected indicate that the monthly sales of a store can be expressed as a linear function the percentage of high school graduates in its customer base? Select the correct statisticaly hypotheses.

A. H0:βˆ1≥0HA:βˆ1<0H0:β^1≥0HA:β^1<0
B. H0:β1=0HA:β1≠0H0:β1=0HA:β1≠0
C. H0:β1=0HA:β1<0H0:β1=0HA:β1<0
D. H0:βˆ1≥0HA:βˆ1≠0H0:β^1≥0HA:β^1≠0
E. H0:β1≥0HA:β1>0H0:β1≥0HA:β1>0
F. H0:βˆ1=0HA:βˆ1>0H0:β^1=0HA:β^1>0

(d) Using the FF-test, test the statistical hypotheses determined in (c). Find the value of the test statistic, using two decimals in your answer.

FcalcFcalc =

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(e) Testing the statistical hypotheses in (c) at α=0.05α=0.05, you can conclude from this data that the  ? monthly sales of a store percentage of customer base that are high school graduates   ? can cannot  be expressed as a linear function of the  ? monthly sales of a store percentage of customer base that are high school graduates .


(f) Can you infer from this data that an increase of 1% to the percentage of high school graduates in the customer based will lead to an mean/average increase in the store's monthly sales by more than $50,000?


(i) Find the value of the test statistic, use two decimal places in your answer.

TcalcTcalc =

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(ii) Find the PP-value of the result, using three decimals.

PP-value =

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(g) A store located at a local mall has recently discovered that 90% of its customer base has a high school diploma. With 95% confidence, estimate this store's monthly sales for the current month.
Note: You will need ∑38i=1PercentHSGradsi=2935.17∑i=138PercentHSGradsi=2935.17 and ∑38i=1PercentHSGrads2i=228777∑i=138PercentHSGradsi2=228777


Lower Bound =

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$1000s (use one decimal in your answer)

Upper Bound =

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$1000s (use one decimal in your answer)

(h) A residual plot of the regression was consulted.



What does this residual plot say about the condition(s) of the model? Pick the most appropriate answer.

A. The variance in the monthly sales is not the same for all stores with different proportions of high school graduates in their respective customer base.
B. The variance in the monthly sales is the same for all stores with different proportions of high school graduates in their respective customer base.
C. The distribution in the monthly sales is Normally distributed.
D. The distribution in the monthly sales is not Normally distributed.
E. The variation in the proportion of the customer base that are high school graduates is the same for all stores.
F. The variation in the proportion of the customer based that are high school graduates is not the same for all stores.

COULD YOU ANSWER ONLY ON QUESTION H, G, E, F

Background
Hotel One is one of the two hotels serving Dayville, a small town in the US Midwest. Fifty percent of its customers are out-of-town visitors to the local college, 30 percent are visiting Dayville for business purposes, and the remaining 20 percent of Hotel One’s customers are leisure travelers. The hotel is within one mile from campus, approximately four miles from the city center, and eight miles from the airport. It is easy to reach by car, taxi, or city bus. You are a manager of Hotel One. Your facility consists of 150 rooms, all of which are standard rooms with two double beds. Your only competitor in Dayville, The Other Hotel, has fewer rooms (100), but 20 of their rooms are luxury suites with king beds and a sofa couch (the other 80 are standard rooms with two double beds). This is the extent of the information provided to you at this point.

Assignment
In order to better understand your unit’s operating environment, you are asked to provide your estimate of the demand equation that would account for various factors that affect your customer traffic. This will be done by using regression techniques. The first step in estimating a demand equation is to determine what variables will be used in the regression. Please provide detailed answers to the following questions:
1. What do you think should be the dependent variable in your demand equation? What units of measurement for that variable are you going to adopt? Please provide a detailed explanation for these choices.
2. Please request information about up to five independent (explanatory) variables for your demand equation. For each variable you request, (i) provide reasons why you expect it to be
important for your analysis and (ii) explain the expected sign of the relationship between the proposed independent variable and your proposed dependent variable.
3. Show the exact demand equation you are proposing to estimate.

Trevor is interested in purchasing the local hardware/sporting goods store in the small town of Dove Creek, Montana. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 55% of the business days it is open. Estimate the probability that the store will gross over $850 for the following. (Round your answers to three decimal places.)

(a) at least 3 out of 5 business days

(b) at least 6 out of 10 business days

(c) fewer than 5 out of 10 business days

(d) fewer than 6 out of the next 20 business days

If the outcome described in part (d) actually occurred, might it shake your confidence in the statement p = 0.55? Might it make you suspect that p is less than 0.55? Explain.

Yes. This is unlikely to happen if the true value of p is 0.55.

Yes. This is likely to happen if the true value of p is 0.55.

No. This is unlikely to happen if the true value of p is 0.55.

No. This is likely to happen if the true value of p is 0.55.

(e) more than 17 out of the next 20 business days

If the outcome described in part (e) actually occurred, might you suspect that p is greater than 0.55? Explain.

Yes. This is unlikely to happen if the true value of p is 0.55.

Yes. This is likely to happen if the true value of p is 0.55.

No. This is unlikely to happen if the true value of p is 0.55.

No. This is likely to happen if the true value of p is 0.55.

Problem 2. Suppose there is only one yoga studio in town. The marginal cost of producing yoga sessions is as follows: MC=12. The yoga studio faces the following market demand function: Q=20-(1/2)P, and marginal revenue MR=40-4Q.

1. (6 points) Calculate the profit-maximizing price, output, and profit for the yoga studio.

2. (bonus: 3 points) Graph the market demand curve, the studio's marginal revenue and marginal cost curves, indicating profit, price, and quantity at the profit-maximizing level of output.

3. (4 points) Suppose that the owner of the studio has determined that each of her 30 regulars has the following identical demand for yoga sessions: Q=4-(1/4)P. The studio's marginal revenue from one of these consumers, then, is MR=16-8Q. The owner wants to use a two-part pricing scheme based on this information, in which she charges admission to the studio and a per-session price. The studio's costs have not changed in this scenario. How should the owner set the admission fee and the per-session price? How many sessions will she sell, and what will her profit be?

1. Multiple Regression:  A rental property owner in a midsized town of Appleton wants to determine the appropriate rent to charge in a new apartment complex and therefore wants to model the relationship between property Rent (Y)in dollars, the number of Bedrooms(x1), Square foot(x2) area of each apartment and whether the apartment comes with a Dishwasher(x3). Dishwasher is coded using a dummy variable that takes the value of 1 if the apartment comes with a dishwasher and 0 if it doesn’t. Using a random sample ofn = 60apartments in the area the owner obtains the following regression output. (15 points)

Model:   Y = b₀+ b₁Bedrooms+b₂Sqft+ b₃Dishwasher Dummy+e

Dishwasher Dummy 1   if Dishwasher included
                                   0   Otherwise

1. Write the equation for the regression equation in terms of the variables and the estimated coefficients? (include the t-stat below each coefficient value).

2. The value of R² and adjusted R², measure the goodness of fit of the model. Which is the appropriate estimate to use for multiple regression analysis? Explain what it means.

3. Given that Rent is measured in dollars, interpret the relationship between (a) number of Bedrooms and Rent and (b) Dishwasher and Rent. (Give your answerin the correct units)

4. Use the estimated equation in (A) to predict the Rent on a 2 Bedroom apartment, with 915 sqft area.
   1. With no Dishwasher

2. With Dishwasher

5. Conduct a test of hypothesis using a= 0.05, forb₁, b₂and b₃. Compare the model t-stats for each independent variable against the critical t-valuefor a 2-sided test and determine if the variable is significant in explaining home price.

                                          H₀:

                                          H_A:

Criticalt-value=

                        Show on a graph:

6. Use the t-statsfrom the Excel output to determine if you should accept or reject the H₀forb_1,b₂andb_3.

Are number of bedrooms significant in explaining apartment Rent? Square Feet Area?  

3. Breakdown of a cartel agreement Consider a town in which only two residents, Sam and Teresa, own wells that produce water safe for drinking. Sam and Teresa can pump and sell as much water as they want at no cost. For them, total revenue equals profit. The following table shows the town's demand schedule for water. Price Quantity Demanded Total Revenue (Dollars per gallon) (Gallons of water) (Dollars) 3.00 0 0 2.75 50 $137.50 2.50 100 $250.00 2.25 150 $337.50 2.00 200 $400.00 1.75 250 $437.50 1.50 300 $450.00 1.25 350 $437.50 1.00 400 $400.00 0.75 450 $337.50 0.50 500 $250.00 0.25 550 $137.50 0 600 0 Suppose Sam and Teresa form a cartel and behave as a monopolist. The profit-maximizing price is $ per gallon, and the total output is gallons. As part of their cartel agreement, Sam and Teresa agree to split production equally. Therefore, Sam's profit is $ , and Teresa's profit is $ . Suppose that Sam and Teresa have been successfully operating as a cartel. They each charge the monopoly price and sell half of the monopoly quantity. Then one night before going to sleep, Sam says to himself, "Teresa and I aren't the best of friends anyway. If I increase my production to 50 gallons more than the cartel amount, I can increase my profit even though her profit goes down. I will do that starting tomorrow." After Sam implements his new plan, the price of water to $ per gallon. Given Teresa and Sam's production levels, Sam's profit becomes $ and Teresa's profit becomes $ . Because Sam has deviated from the cartel agreement and increased his output of water to 50 gallons more than the cartel amount, Teresa decides that she will also increase her production to 50 gallons more than the cartel amount. After Teresa increases her production, Sam's profit becomes $ , Teresa's profit becomes $ , and total profit (the sum of the profits of Sam and Teresa) is now $ . True or False: Based on the fact that both Sam and Teresa increased production from the initial cartel quantity, you know that the output effect was larger than the price effect at that quantity. True False Note that Sam and Teresa started by behaving cooperatively. However, once Sam decided to cheat, Teresa decided to cheat as well. In other words, Teresa's output decisions are based on Sam's actions.

This behavior is an example of

On July 1, 2019, the first day of its 2020 fiscal year, the Town of Bear Creek issued at par $4,200,000 of 8 percent term bonds to renovate a historic wing of its main administrative building. The bonds mature in five years on July 1, 2024. Interest is payable semiannually on January 1 and July 1.

As illustrated in the table below, a sinking fund is to be established with equal semiannual additions made on June 30 and December 31. Cash for the sinking fund additions and the semiannual interest payments will be transferred from the General Fund shortly before the due dates. Investment earnings are added to the investment principal.

Required

1.      a-1. Prepare journal entries in the debt service fund for the following: (If no entry is required for a transaction/event, select "No Journal Entry Required" in the first account field. Do not round intermediate calculations.)

On July 1, 2019, record the budget for the fiscal year ended June 30, 2020. Include all inter-fund transfers to be received from the General Fund during the year. An appropriation should be provided only for the interest payment due on January 1, 2020.

A, Term Bond Debt Service Fund:

On December 28. 2019, the General Fund transferred $517,882 to the debt service fund. The addition to the sinking fund was immediately invested in 8 percent certificates of deposit.

B1. Tern Bond Debt Service Fund: Record the transfer fro the general fund to the debt service fund

B2. Record the investment in the certificates of deposit.

On December 28, 2019, the city issued checks to bondholders for the interest payment due on January 1, 2020.

C. Term Bond Debt Service Fund:

On June 27, 2020, the General Fund transferred $517, 822 to the debt service fund. The addition for the sinking fund was invested immediately in 8 percent certificates of deposit.

D1. Term Bond Service Fund: Record the transfer from the general fund to the debt service fund.

D2. Record the investment in the certificates of deposit

Actual interest earned on sinking fund investments at year end (june 30, 2020) was the same as the amount budgeted in the table. This interest adds to the sinking fund balance.

E. Term Bond Service Fund

Currently Sam and Carla have the only taxi services in a small town. Both Sam and Carla are thinking about discounting their respective fares by 20% to attract more business.  

The possible outcomes of this game are as follows.

First: Sam offers discounts, while Carla does not, which will result in Sam earning $400 in profit and Carla earning $800 in profit.

Second: Sam and Carla both offer discounts, which will result in Sam earning $200 in profit and Carla earning $500 in profit.

Third: Sam and Carla both do not offer discounts, which will result in Sam earning $100 in profit and Carla earning $1,000 in profit.

Fourth: Carla offers discounts, while Sam does not, which will result in Sam earning $60 in profit and Carla earning $700 in profit.

a) Please construct a payoff matrix for Sam and Carla uses the outcomes above. (You can use the Table Function in Word to create a payoff matrix.)

b) Does Sam have a dominant (optimal) strategy? Please explain your answer.

c) Does Carla have a dominant (optimal) strategy? Please explain your answer

D) Is there an equilibrium (Nash Equilibrium) solution to this problem where we can predict the strategy of both Sam and Carla? Please explain your reasoning.

A city commissioner in Brownsville believe his police officers are underpaid compared with a neighboring town. A random sample of 17 police officers in Brownsville has a mean annual income of $35,800 and a standard deviation of $7,800. In Greensville, a random sample of 15 police officers has a mean annual income of $35,100 and a standard deviation of $7,375. Test the claim at α = 0.01 that the mean annual income in Brownsville is less than Greensville. Assume the population variances are equal.

a.What is the standard error?

b.What is the test statistic?

c.Reject or fail to reject?