Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (x) and the amount of fire damage, in thousands of dollars (y). The MegaStat output is reported below.

a-1. Write out the regression equation. (Round your answers to 3 decimal places.)

a-2. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage?

2. How much damage would you estimate for a fire 9 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)

c-1. Determine and interpret the coefficient of determination. (Round your answer to 3 decimal places.)

c-2. Fill in the blank below. (Round your answer to one decimal place.)

____% of the variation in damage is explained by variation in distance.

d-1. Determine the correlation coefficient. (Round your answer to 3 decimal places.)

d-3. How did you determine the sign of the correlation coefficient?

e-1. State the decision rule for 0.01 significance level: H₀ : ρ = 0; H₁ : ρ ≠ 0. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)

e-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

e-3. Is there any significant relationship between the distance from the fire station and the amount of damage? Use the 0.01 significance level.

You are a real estate developer and are trying to determine the EMV of your net commission from a sales call to a potential purchaser.

Assume that your transportation cost is $1.45 per mile

Assume that the sales call is 70 miles round trip

Assume that your transportation time is 2.25 minutes per mile

Assume that the value of your time for transportation is $55.00 per hour

Assume that it will take 3 hours to meet with the potential purchaser

Assume that the value of your time for the customer meeting is $150.00 per hour

Assume that you will have a 19% chance of a successful sales call (sales call #1)

If sales call #1 is successful,

you will sell a house valued at $275,000 with likelihood = 55%

you will sell a house valued at $300,000 with likelihood = 35%

you will sell a house valued at $425,000 with likelihood = 10%

Assume that your commission will be 2.5% of the value of the house if sales call #1 is successful.

a) What is the expected cost (time and transportation) of sales call #1?

b) Without assuming that the sales call will be successful (that is, it may or may not be a success), what is the expected gross commission of sales call #1 (do not net out the expected costs)?

Suppose you have a second possible sales call (sales call #2). Assume that the expected cost remains the same and that the commission rate remains 2.5%, but that the following information is the different information for sales call #2.

Assume that you will have a 12% chance of a successful sales call (sales call #2) If sales call #2 is successful,

you will sell a house valued at $285,000 with likelihood = 45%

you will sell a house valued at $320,000 with likelihood = 25%

you will sell a house valued at $355,000 with likelihood = 30%

c) Assuming that your sales call is successful, look at the worst possible outcome for each decision and choose the decision that has the best (or least bad) of these.

This file is from a statistics textbook and

provides information on over 100 recently sold homes in a town in Arizona (fictional). The variables that

are included are:

Price: Sales prices in thousands of dollars

Bedrooms: Number of bedrooms

Baths: Number of bathrooms

Size: Size of the house measured in square feet

Pool: Variable is 0 if no pool, and 1 if there is a pool

Garage: Variable is 0 if no garage, and 1 if there is a garage

Distance: This is the number of miles that the house is from city center

Township: There are five townships in the town. This identifies the township the house is in

Part 1: Identify whether each variable is qualitative or quantitative. Then identify whether each

variable is nominal, ordinal, interval, or ratio.

Part 2: Use statistical techniques to provide a summary of the homes in this town. This can include

summary statistics and/or graphs. Think about what type of information is contained in each variable

(part 1) before you select summary techniques.

Part 3: Choose two townships and compare some aspects of the homes in each township. Please

consider both qualitative and quantitative characteristics. If a variable is quantitative please consider

measures of center and measures of dispersion when possible.

Liam is a 17-year-old male who is being seen by his family physician for his annual physical examination. Liam’s sexual maturation rating is estimated to be 3. He weighs 114 lbs and stands 5’6” tall.

When he was 16 y.o., his height was 5’5” and weight was 106 lbs.  

At 15 y.o., Liam was 5’3” tall and weighed 98lbs.  

During the visit, Liam reports that he has been experimenting with a vegan diet since his visit last year. He explains that he thinks it is a healthier way to eat and states that he avoids milk, beef, and pork eats poultry or fish once every two weeks and eats cheese 3-4x/wk. Breakfast is usually cold cereal with almond milk because he heard that was a healthy milk alternative. He likes pasta, pizza, and salad, which he eats almost every day.  

For exercise, he runs 3 miles 2x/wk, plays basketball with friends after school 3x/wk for an hour, and lifts weights in his garage for 45 min 5x/wk.  

He says he would like to gain muscle and grow taller.  

3. What clarifying questions would you like to ask Liam about his current behaviors? List 3.

4. If there is protein a concern in Liam’s diet, why? Estimate his RDA and use evidence to support your position.

5. Given Liam’s diet and exercise patterns, which dietary components may he be deficient in? For each dietary component, list possible food sources that are appropriate for his current eating pattern.

6. There are both health benefits and costs of eating mostly plants. How might his current way of eating affect Liam’s growth and maturation?

7. Is it necessary to assess Liam for the presence of an eating disorder? Provide support for your answer.

Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (x) and the amount of fire damage, in thousands of dollars (y). The MegaStat output is reported below

-1. Write out the regression equation. (Round your answers to 3 decimal places.) a-2. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage? How much damage would you estimate for a fire 9 miles from the nearest fire station? (Round your answer to the nearest dollar amount.) c-1. Determine and interpret the coefficient of determination. (Round your answer to 3 decimal places.) c-2. Fill in the blank below. (Round your answer to one decimal place.) d-1. Determine the correlation coefficient. (Round your answer to 3 decimal places.) d-2. Choose the right option. d-3. How did you determine the sign of the correlation coefficient? e-1. State the decision rule for 0.01 significance level: H0 : ρ = 0; H1 : ρ ≠ 0. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.) e-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.) e-3. Is there any significant relationship between the distance from the fire station and the amount of damage? Use the 0.01 significance level. rev: 10_12_2017_QC_CS-102203

Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (x) and the amount of fire damage, in thousands of dollars (y). The MegaStat output is reported below.

1. Write out the regression equation. (Round your answers to 3 decimal places.)

2. a-2. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage?

3. How much damage would you estimate for a fire 6 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)

4. c-1. Determine the coefficient of determination. (Round your answer to 3 decimal places.)

5. c-2. Fill in the blank below. (Round your answer to one decimal place.)

6. d-1. Determine the correlation coefficient. (Round your answer to 3 decimal places.)

7. d-2. Choose the right option.

8. d-3. How did you determine the sign of the correlation coefficient?

9. e-1. State the decision rule for 0.01 significance level: H₀ : ρ = 0; H₁ : ρ ≠ 0. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)

10. e-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

11. e-3. Is there any significant relationship between the distance from the fire station and the amount of damage? Use the 0.01 significance level.

On Friday afternoon you received a call from a gentleman who identified himself as the chief executive officer of a firm in a small city about 100 miles from your headquarters. He wanted to charter an aircraft to make a trip to a small U.S. border town. He assured you that you would not be required to fly over the border into a foreign country or deal with customs agents. The trip would depart tomorrow (Saturday) evening, make a two-hour stop at the town’s airport, and return sometime after midnight Sunday morning.

The caller cautioned you about the confidentiality of the trip and requested that your two “most closed-mouthed” pilots fly the charter. In reply to some serious and repeated questions concerning the mission and legality of the trip and/or cargo, the caller assured you that the trip was for legal business purposes, and no contraband would be involved. He alluded to “a highly sensitive business matter” that would have an enormous effect on his firm if “the parties can agree.”

The aircraft you would have available to send is in good condition and its maintenance schedule is up-to-date; thus the trip would not endanger the readiness of the aircraft for its normal schedule the following Sunday. The prospective customer has offered you a fee that would net your firm $5,000 profit above the direct costs. The fee is somewhat large, considering the length of the trip, but the caller offered it, and you did not object.

You couldn’t find information about the firm online. Because it is late in the day on a Friday, you aren’t able to research the firm any further.

Your director of marketing is urging you to take the charter because of the potential profit and future business this firm might provide. “I’ve heard of the company. They’re in air conditioning or something like that. I’ve also heard they’re either trying to acquire another company, or they’re about to be acquired. This might be the final closing of the deal.”

1. Take the charter trip.

2. Do not take the charter trip.

A realtor studies the relationship between the size of a house (in square feet) and the property taxes (in $) owed by the owner. The table below shows a portion of the data for 20 homes in a suburb 60 miles outside of New York City.

a-1. Calculate the sample correlation coefficient r_xy. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

a-2. Interpret r_xy.

a. The correlation coefficient indicates a positive linear relationship.

b. The correlation coefficient indicates a negative linear relationship.

c. The correlation coefficient indicates no linear relationship.

b. Specify the competing hypotheses in order to determine whether the population correlation coefficient between the size of a house and property taxes differs from zero.

a. H₀: ρ_xy = 0; H_A: ρ_xy ≠ 0

b. H₀: ρ_xy ≥ 0; H_A: ρ_xy < 0

c. H₀: ρ_xy ≤ 0; H_A: ρ_xy > 0

c-1. Calculate the value of the test statistic.

c-2. Find the p-value.

a. p-value < 0.01

b. p-value  0.10

c. 0.05  p-value < 0.10

d. 0.02  p-value < 0.05

e. 0.01  p-value < 0.02

d. At the 1% significance level, what is the conclusion to the test?

a. Reject H₀; we can state size and property taxes are correlated.

b. Reject H₀; we cannot state size and property taxes are correlated.

c. Do not reject H₀; we can state size and property taxes are correlated.

d. Do not reject H₀; we cannot state size and property taxes are correlated.

1. A state’s Division of Motor Vehicles (DMV) claims that 60% of all teens pass their driving test on the
first attempt. An investigative reporter examines an SRS of the DMV records for 125 teens; 56 of them
passed the test on their first try. Is there convincing evidence at the α=0.01 significance level that the
DMV’s claim is lower?

2. In a recent year, 65% of first-year college students responding to a national survey identified “being
very well-off financially” as an important personal goal. A state university finds that 102 of an SRS of
200 of its first-year students say that this goal is important. Is there convincing evidence at
the α=0.05 significance level that the proportion of all first-year students at this university who think
being very well-off is important differs from the national value of 65%?

3. Every road has one at some point—construction zones that have much lower speed limits. To see if
drivers obey these lower speed limits, a police officer uses a radar gun to measure the speed (in miles
per hour, or mph) of a random sample of 10 drivers in a 25 mph construction zone. Here are the data:
27 33 32 21 30 30 29 25 27 34
Is there convincing evidence at the α=0.01 significance level that the average speed of drivers in this
construction zone is greater than the posted speed limit?

4. A school librarian purchases a novel for her library. The publisher claims that the book is written at a fifth-grade reading level, but the librarian suspects that the reading level is lower than that. The librarian selects a random sample of 45 pages and uses a standard readability test to assess the reading level of each page. The mean reading level of these pages is 4.8 with a standard deviation of 0.6. Do these data give convincing evidence at the α=0.01 significance level that the average reading level of this novel is less than 5?

Short Case: Decisions - what to do?
There are some individuals that believer these ratios are too heavily relied upon and that they do not truly assess an organization's financial status. In reality, they provide a comparison of where the organization stands to other similar organization within the same industry. If a 100 bed hospital on average has only 50 beds filled each day, there is a possibility that the hospital is generating revenue below its projected budget and has had to reduce staffing. It would not make good business sense to staff for 100 patients when at best you would only occupy 50 of the 100 available beds.
It is probably safe to assume that this hospital is not in a profitable state based on the number of occupied hospital beds? In its best days, it was the only hospital in the area and now there are 2 competing hospitals. The mission of the hospital has not changed since it opened; it is "to be the best primary hospital provider within 60 miles". It offers a full range of ER and hospital care (x-rays, MRIs, clinics, specialty care, etc.)
While the hospital does have an ER, it is not a Level I trauma hospital. Additionally, due the a significant loss of jobs within the local community, many of the residents no longer have health insurance and/or are on Medicare or Medicaid.
I know there is little information to work from, but give it a try.


Short Case
1. As you are the CEO, would you try to turn this situation around or prepare the hospital for closure.
2. What ratios would you use as part of your analysis and why?
3. What are some of the other areas in which the hospital would need to consider reductions to meet its budget. What are some of the other options that the hospital could pursue to address its financial status?
4. Would this hospital be a good candidate for a merger/acquisition? Please explain the rationale for your choice and identify what assumptions your decision was based on.