The data in the table, from a survey of resort 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.

• First make a linear equation using linear regression on your calculator where x = price and y = occupancy rate.
• Convert occupancy rate to quantity of rooms in a 200-room hotel.
• Write down a revenue function for a 200-room hotel.
• What price per day will maximize the daily off-season revenue for a typical 200-room hotel? Use Calculus to determine the maximum.
• If this 200-room hotel has daily operating costs of $5510 plus $30 per occupied room. What price will maximize the daily profit during the off-season? Again use calculus to determine the maximum

More detailed instructions are given on page 690 of the textbook (12th edition).

A survey of 1060people who took trips revealed that 94 of them included a visit to a theme park. Based on those survey results, a management consultant claims that less than 11 % of trips include a theme park visit. Test this claim using the ?=0.01significance level.

(a) The test statistic is ___

(b) The P-value is ___

(c) The conclusion is  

A. There is sufficient evidence to support the claim that less than 11 % of trips include a theme park visit.
B. There is not sufficient evidence to support the claim that less than 11 % of trips include a theme park visit.

Independent random samples, each containing 90 observations, were selected from two populations. The samples from populations 1 and 2 produced 36 and 26 successes, respectively.
Test ?0:(?1−?2)=0against ??:(?1−?2)>0 Use ?=0.1

(a) The test statistic is ___

(b) The P-value is ___

(c) The final conclusion is
A. There is not sufficient evidence to reject the null hypothesis that (?1−?2)=0
B. We can reject the null hypothesis that (?1−?2)=0 and conclude that (?1−?2)>0

Consider a new hotel deciding on cleaning staff hiring for the upcoming season. Cleaning times depend on whether it is a stay-over room or a check-out. Suppose that a guest will check-out on a given day with probability 40%. From your experience in similar hotels you estimate that a stay-over room cleaning time is well-described with normal distribution with average 15 minutes and standard deviation 1 minute. Check-out room cleaning time is also normal but with average 30 minutes and standard deviation 10 minutes.

i. Consider an occupied room (stay-over or check-out), what is the average cleaning time for such a room?

ii. Find the variance for the cleaning time for an occupied room.

iii. Suppose that the hotel has 200 rooms, and you estimate that on a given day a room will be occupied with probability 90%. Only occupied rooms need cleaning. Find the average total cleaning time for the hotel. iv. Find the variance of the total cleaning time for the hotel.

Hints: remember var(X) = EX^2 − (EX)^2 .

1, An engineer wanted to determine how the weight of a car affects gas mileage. The accompanying data represent the weights of various domestic cars and their gas mileage in the city for a certain model year. Suppose that we add Car 12 to the original data. Car 12 weighs 3,305 pounds and gets 19 miles per gallon. Complete parts​(a) through​ (f) below.

(b) Compute the linear correlation coefficient with Car 12 included.

The linear correlation coefficient with Car 12 included is r =

​(Round to three decimal places as​ needed.)

(c) Compare the linear correlation coefficient of the part? (b) with the linear correlation coefficient for the original data. Why are the results here? reasonable?

i) The correlation coefficient changed significantly when Car 12 was added. This is reasonable since Car 12 does not follow the pattern of the original data.

ii) The correlation coefficients both indicate a strong negative correlation. This is reasonable since Car 12 does not follow the pattern of the original data.

iii) The correlation coefficients both indicate a strong negative correlation. This is reasonable since Car 12 roughly follows the pattern of the original data.

d) Now suppose that we add Car 13? (a hybrid? car) to the original data? (remove Car? 12). Car 13 weighs 2,890 pounds and gets 60 miles per gallon. Draw the scatter diagram with Car 13 included.

e) Compute the linear correlation coefficient with Car 13 included.

2, Researchers wondered whether the size of a​ person's brain was related to the​individual's mental capacity. They selected a sample of 5 females and 5 males and measured their MRI counts and IQ scores. The data is reported to the right. Complete parts ​(a) through ​(d) below.

Critical Values for Correlation Coefficient

​(a) Draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable. Choose the correct diagram below.

(b) Compute the linear correlation coefficient between MRI count and IQ. Are MRI count and IQ linearly​ related? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

​(Round to three decimal places as​ needed.)

A.​Yes, MRI count and IQ are linearly related since the linear correlation coefficient is

B.​No, MRI count and IQ are not linearly related since the linear correlation coefficient is

​(c) Draw a scatter​ diagram, but use a different plotting symbol for each gender. Choose the correct diagram below.

​(d) Compute the linear correlation coefficient between MRI count and IQ for females. Compute the linear correlation coefficient between MRI count and IQ for males.

The linear correlation coefficient for females is

The linear correlation coefficient for males is

​(Round to three decimal places as​ needed.)

A) Mountain Dental Services is a specialized dental practice whose only service is filling cavities. Mountain has recorded the following for the past nine months: ( answered in2 decimal)

Required:

1. Use the high-low method to estimate total fixed cost and variable cost per cavity filled.

2. Using these estimates, calculate Mountain’s total cost for filling 400 cavities.

B) Riverside Inc. makes one model of wooden canoe. Partial information for it follows: (answered in 2 decimal)

Required:

1. Complete the table.

3. Suppose Riverside sells its canoes for $518 each. Calculate the contribution margin per canoe and the contribution margin ratio.

4. Next year Riverside expects to sell 845 canoes. Complete the contribution margin income statement for the company.

C) Riverside Inc. makes one model of wooden canoe. Partial information for it follows: (answered in 2 decimals)

Riverside sells its canoes for $460 each. Next year Riverside expects to sell 1,000 canoes.

Required:

Complete the Riverside’s contribution margin income statement for each independent scenario. Assuming each scenario is a variation of Riverside’s original data. (Round your unit contribution margin and contribution margin ratio to 2 decimal places (i.e. .1234 should be entered as 12.34%) and all other answers to the nearest dollar amount.)

D) Joyce Murphy runs a courier service in downtown Seattle. She charges clients $0.64 per mile driven. Joyce has determined that if she drives 2,750 miles in a month, her total operating cost is $875. If she drives 3,850 miles in a month, her total operating cost is $1,139.

Required:

1. Using the high-low method, determine Joyce’s variable and fixed operating cost components.

2. Complete the contribution margin income statement for Joyce’s service assuming she drove 1,950 miles last month. (Assume this falls within the relevant range of operations).

D) The following information pertains to the first year of operation for Crystal Cold Coolers Inc.:

Required:

Prepare Crystal Cold’s full absorption costing income statement and variable costing income statement for the year.

1. The average production cost for major movies is 57 million dollars and the standard deviation is 22 million dollars. Assume the production cost distribution is normal. Suppose that 46 randomly selected major movies are researched. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. For a single randomly selected movie, find the probability that this movie's production cost is between 51 and 56 million dollars.
4. For the group of 46 movies, find the probability that the average production cost is between 51 and 56 million dollars.

2. Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 1.1 month. 18 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X ~ N( , )  
2. What is the distribution of x¯? x¯ ~ N( , )
3. What is the probability that one randomly selected person learned to walk when the person was between 10 and 12.5 months old?
4. For the 18 people, find the probability that the average age that they learned to walk is between 10 and 12.5 months old.
5. For part d), is the assumption that the distribution is normal necessary? Yes or No
6. Find the IQR for the average first time walking age for groups of 18 people.
   Q1 = ______ months
   Q3 = ______ months
   IQR: ______ months

3. The average number of miles (in thousands) that a car's tire will function before needing replacement is 72 and the standard deviation is 12. Suppose that 8 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of X? X ~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 78.2 and 84.2.
4. For the 8 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 78.2 and 84.2.

4. The lengths of adult males' hands are normally distributed with mean 188 mm and standard deviation is 7.2 mm. Suppose that 17 individuals are randomly chosen. Round all answers to 4 decimal places where possible.

1. What is the distribution of x¯? x¯ ~ N( , )
2. For the group of 17, find the probability that the average hand length is more than 187.
3. Find the third quartile for the average adult male hand length for this sample size.

5. Suppose that the average number of Facebook friends users have is normally distributed with a mean of 125 and a standard deviation of about 55. Assume fourteen individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of x¯? x¯ ~ N( , )
2. For the group of 14, find the probability that the average number of friends is less than 107.
3. Find the first quartile for the average number of Facebook friends

6. The amount of syrup that people put on their pancakes is normally distributed with mean 57 mL and standard deviation 9 mL. Suppose that 41 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

1. What is the distribution of X? X ~ N( , )
2. What is the distribution of x¯? x¯ ~ N( , )
3. If a single randomly selected individual is observed, find the probability that this person consumes is between 57.7 mL and 59.2 mL.
4. For the group of 41 pancake eaters, find the probability that the average amount of syrup is between 57.7 mL and 59.2 mL

For several decades, it was a common practice in Southern California for houses to be built with pools in the backyard (as any airplane flight which ends at a Southern California airport will reveal). Now, however, that practice may be changing, possibly because of the recent demand for landscaped homes, which experts believe help reduce pollution. A recent study examined a random sample of

161

houses built in Southern California between 1950 and 1985 and an independent, random sample of

80

houses built in Southern California from 1992 to the present. The sample of houses built in 1950-1985 contained

72

houses with pools, and the sample of houses built from 1992-present contained

32

houses with pools. Based on this survey, can we conclude, at the

0.1

level of significance, that the proportion

p1

of all Southern California houses built in 1950-1985 that were built with pools is greater than the proportion

p2

of all Southern California houses built from 1992-present that were built with pools?

Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

One of the central predictions of neo-classical macroeconomic growth theory is that an increase in the growth rate of the population causes at first a decline the growth rate of real output per capita, but that subsequently the growth rate returns to its natural level, itself determined by the rate of technological innovation. The intuition is that, if the growth rate of the workforce increases, then more has to be saved to provide the new workers with physical capital. However, accumulating capital takes time, so that output per capita falls in the short run.

Under the assumption that population growth is exogenous, a number of regressions of the growth rate of output per capita on current and lagged population growth were performed, as reported below. (A constant was included in the regressions but is not reported. HAC standard errors are in brackets. BIC is listed at the bottom of the table).

Regression of Growth Rate of Real Per-Capita GDP on Lags of Population Growth, United States, 1825-2000

(a) Which of these models is favored by the information criterion?
(b) How consistent are these estimates with the theory? Is this a fair test of the theory? Why or why not?
(c) Can you think of any improved data to test the theory?