Even within a particular chain of hotels, lodging during the summer months can vary substantially depending on the type of room and the amenities offered. Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for 50 billing statements from each of the computer databases of each of the three hotel chains are given in the table.

Hotel A Hotel B Hotel C

Sample average ($) 145 160. 125

Sample standard deviation 17.6 22.6. 12.5

(a) Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel C chains. (Round your answers to two decimal places.)

Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Service statistics, 46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows park entrance, 24.3% of visitors entered through the Fall River park entrance, 6.3% of visitors entered through the Grand Lake park entrance, and 22.7% of visitors had no recorded point of entry to the park.† Consider a random sample of 175 Rocky Mountain National Park visitors. Use the normal approximation of the binomial distribution to answer the following questions. (Round your answers to four decimal places.)

(a)
What is the probability that at least 65 visitors had a recorded entry through the Beaver Meadows park entrance?

(b)
What is the probability that at least 60 but less than 70 visitors had a recorded entry through the Beaver Meadows park entrance?

(c)
What is the probability that fewer than 11 visitors had a recorded entry through the Grand Lake park entrance?

(d)
What is the probability that more than 40 visitors have no recorded point of entry?

Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Service statistics, 46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows park entrance, 24.3% of visitors entered through the Fall River park entrance, 6.3% of visitors entered through the Grand Lake park entrance, and 22.7% of visitors had no recorded point of entry to the park.† Consider a random sample of 175 Rocky Mountain National Park visitors. Use the normal approximation of the binomial distribution to answer the following questions. (Round your answers to four decimal places.)

(a)

What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?

(b)

What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?

(c)

What is the probability that fewer than 11 visitors had a recorded entry through the Grand Lake park entrance?

(d)

What is the probability that more than 40 visitors have no recorded point of entry?

Universe Studios Sentiasa is a theme park licensed from a major Bollywood studio. Customers pay a fixed fee to enter the park where they can participate in a variety of activities such as riding roller-coasters, playing on slides and purchasing themed souvenirs from gift shops.

Customers purchase tickets to enter the theme park from ticket offices located outside the park. Tickets are only valid on the day of purchase. Adults and children are chargedthe same price for admission to the park. Tickets are preprinted and stored in each ticket office. Tickets are purchased using either cash or credit cards. Each ticket has a number comprising of two elements - two digits relating to the ticket office followed by six digits to identify the ticket. The last six digits are in ascending sequential order.All cash ticket sales are recorded on a computer showing the amount of each sale and the number of tickets issued. This information is transferred electronically to the accounts office. Cash is collected regularly from each ticket office by two security guards. The cash is then counted by two accounts clerks and banked on a daily basis. The total cash from each ticket office is agreed to the sales information that has been transferred from each office. Total cash received is then recorded in the cash book, and then the general ledger.

The park also accepts Visa and Mastercard. Payments by credit cards are authorised online as the customers purchase their tickets. Computers in each ticket office record the sales information, which is transferred electronically to the accounts office. Credit card sales are recorded for each credit card company in a receivables ledger. When payment is received from the credit card companies, the accounts clerks agree the total sales values to the amounts received from the credit card companies, less the commission payable to those companies. The receivables ledger is updated with the payments received. You are now commencing the planning of the annual audit of Universe Studios Sentiasa .

Required

(a) Identify four (4) risks that could affect the assertion of completeness of sales and cash receipts. [12 marks] (b) Discuss the extent to which substantive procedures could be used to confirm the assertion of completeness of income in Universe Studios Sentiasa. [6 marks] (c) Provide any four (4) substantive analytical procedures that can be used to give assurance on the total income from ticket sales for one day in Universe Studios Sentiasa. [12 marks]

A firm incurred a total fixed cost of $400,000 and total variable cost of $600,000 to produce 50,000 units of output.

What are the average fixed cost (AFC), average variable cost (AVC), and average total cost (ATC)?

The following are the total cost for differing amounts of units of hammers. Units Total Cost 26,200 $975,000 44,100 $1,456,400 18,700 $770,600 27,600 $1,011,100 34,400 $1,197,700 What is the variable cost per unit? Using your answer in the above question, estimate the total cost for 25,000 hammers.

QuadPlex Cinema is the only movie theater in Idaho Falls. The nearest rival movie theater, the Cedar Bluff Twin, is 35 miles away in Pocatello. Thus QuadPlex Cinema possesses a degree of market power. Despite having market power, QuadPlex Cinema is currently suffering losses. In a conversation with the owners of QuadPlex, the manager of the movie theater made the following suggestions: “Since QuadPlex is a local monopoly, we should just increase ticket prices until we make enough profit.”

a. Comment on this strategy. Will it work in short run?

b. Is the Lerner index an appropriate measure for the market power of QuadPlex Cinema? Please explain your answer briefly.

c. What options should QuadPlex consider in the long run?

II. Room Pricing in the Off-Season (Modeling)

The data in the table, from a survey of hotels with comparable rates on Hilton Head Island, show that room occupancy during the off-season (November through February) is related to the price charged for a basic room.

The goal is to use these data to help answer the following questions.

1. What price per day will maximize the daily off-season revenue for a typical hotel in this group if it has  rooms available?

2. Suppose that for this typical hotel, the daily cost is  plus  per occupied room. What price will maximize the profit for this hotel in the off-season?

The price per day that will maximize the off-season profit for this typical hotel applies to this group of hotels. To find the room price per day that will maximize the daily revenue and the room price per day that will maximize the profit for this hotel (and thus the group of hotels) in the off-season, complete the following.

1. Multiply each occupancy rate by  to get the hypothetical room occupancy. Create the revenue data points that compare the price with the revenue, , which is equal to price times the room occupancy.

2. Find an equation that models the revenue, , as a function of the price per day, .

3. Use maximization techniques to find the price that these hotels should charge to maximize the daily revenue.

4. Find a model for the occupancy as a function of the price, and use the occupancy function to create a daily cost function.

5. Form the profit function.

6. Use maximization techniques to find the price that will maximize the profit.

Even within a particular chain of hotels, lodging during the summer months can vary substantially depending on the type of room and the amenities offered. Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for 50 billing statements from each of the computer databases of each of the three hotel chains are given in the table.

(a) Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel C chains. (Round your answers to two decimal places.)
$  to $  

(b) Find a 99% confidence interval for the difference in the average room rates for the Hotel B and the Hotel C chains. (Round your answers to two decimal places.)
$  to $  

(c) Do the intervals in parts (a) and (b) contain the value (μ₁ − μ₂) = 0?

Yes, the interval in part (a) contains (μ₁ − μ₂) = 0.Yes, the interval in part (b) contains (μ₁ − μ₂) = 0.    Yes, both intervals contain (μ₁ − μ₂) = 0.No, neither interval contains (μ₁ − μ₂) = 0.

Why is this of interest to the researcher?

If (μ₁ − μ₂) = 0 is contained in the confidence interval, it is implied that the room rate for one of the hotels was $0.If (μ₁ − μ₂) = 0 is contained in the confidence interval, it is implied that there is no difference in the average room rates for the two hotels.    If (μ₁ − μ₂) = 0 is contained in the confidence interval, it is implied that there was an error in the database records.If (μ₁ − μ₂) = 0 is contained in the confidence interval, it is implied that there is a difference in the average room rates for the two hotels.If (μ₁ − μ₂) = 0 is contained in the confidence interval, it is implied that the average room rate for the two hotels was $0.

(d) Do the data indicate a difference in the average room rates between the Hotel A and the Hotel C chains?

Yes, the data indicate a difference in the average room rates between the Hotel A and the Hotel C chains.No, the data do not indicate a difference in the average room rates between the Hotel A and the Hotel C chains.    

Do the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains?

Yes, the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains.No, the data do not indicate a difference in the average room rates between the Hotel B and the Hotel C chains.   

The Park Manager at Fort Fisher State Park in North Carolina believes the typical park visitor spends at least 90 minutes in the park during summer months. A sample of 18 visitors during the summer months of 2011 revealed the mean time in the park was 96 minutes with a standard deviation of 12 minutes. At the 0.01 significance level, is it reasonable to conclude that the mean time in the park is greater than 90 minutes? What is alpha?