Question Set 2: Two Independent Means

Answer the following questions using the NYC2br.MTW file. You can find this dataset in this assignment in Canvas (i.e., where you downloaded this document and where you’ll upload your completed lab). Data were collected from a random sample of two-bedroom apartments posted on Apartments.com in Manhattan and Brooklyn.

A. What is one type of graph that could be used to compare the monthly rental rates of these two-bedroom apartments in Manhattan and Brooklyn? Explain why this is an appropriate graph. [10 points]

B. Using Minitab Express, Construct the graph you described in part A to compare the Manhattan and Brooklyn apartments in this sample. [10 points]

C. Use the five-step hypothesis testing procedure given below to determine if the mean monthly rental rates are different in the populations of all Manhattan and Brooklyn two-bedroom apartments. If assumptions are met, use a t distribution to approximate the sampling distribution. You should not need to do any hand calculations. Use Minitab Express and remember to include all relevant output. [30 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide to reject or fail to reject the null hypothesis

Step 5: State a real-world conclusion

This is the data set.

Area   Rent   Address
Manhattan   5495   56 W 91st ST
Manhattan   2200   10 W 107th ST
Manhattan   3386   181 W 126th ST
Manhattan   2383   236 W 135th ST
Manhattan   2550   3 W 137th ST
Manhattan   2600   533 W 142nd ST
Manhattan   2600   260 W 171st ST
Manhattan   2150   518 W 204th ST
Manhattan   3200   680 Fort Washington AVE
Manhattan   2200   69 Cooper ST
Manhattan   2199   24 Thayer ST
Manhattan   2950   45 Tiemann PL
Manhattan   2780   510 E 117th ST
Manhattan   2695   314 E 106th ST
Manhattan   2900   320 E 93rd ST
Manhattan   5900   58 W 58th ST
Manhattan   25000   160 Central Park S
Manhattan   15000   30 E 62nd ST
Manhattan   4650   220 E 54th ST
Manhattan   2175   431 E 9th ST
Manhattan   7950   18 W 48th ST
Manhattan   2675   534 W 47th ST
Manhattan   3507   331 W 52nd ST
Manhattan   5195   236 E 47th ST
Manhattan   7750   445 W 35th ST
Manhattan   6883   1050 6th AVE
Manhattan   13754   7 W 21st ST
Manhattan   3995   172 Spring ST
Manhattan   5750   133 2nd AVE
Manhattan   6000   364 E 10 ST
Manhattan   3900   216 Centre ST
Manhattan   3400   167 Mott ST
Manhattan   16000   20 Greene ST
Manhattan   3200   174 Canal ST
Manhattan   4000   196 Stanton ST
Manhattan   8500   46 Warren ST
Manhattan   5950   108 South ST
Manhattan   3600   75 Wall ST
Manhattan   6598   44 Trinity PL
Manhattan   7995   377 Rector PL
Manhattan   6508   41 River TER
Brooklyn   3300   76 Franklin ST
Brooklyn   3150   80 Meserole ST
Brooklyn   4225   224 Wythe AVE
Brooklyn   3256   228 Manhattan AVE
Brooklyn   2500   1421 Dekalb AVE
Brooklyn   2900   381 Myrtle AVE
Brooklyn   4350   9 Old Fulton ST
Brooklyn   5500   365 Bridge ST
Brooklyn   3900   117 Congress ST
Brooklyn   2600   224 Sachett ST
Brooklyn   4358   280 Ashland PL
Brooklyn   3125   229 5th AVE
Brooklyn   3900   753 Carroll ST
Brooklyn   3450   497 Saint Marks AVE
Brooklyn   2000   544 Franklin AVE
Brooklyn   2575   237 Troy AVE
Brooklyn   2300   223 Rockaway AVE
Brooklyn   2150   231 Amboy ST
Brooklyn   2000   789 Belmont AVE
Brooklyn   1800   542 E 93rd ST
Brooklyn   4213   125 Parkside AVE
Brooklyn   12500   3 Pierrepont PT
Brooklyn   5000   135 Willow ST
Brooklyn   2500   224 22nd ST
Brooklyn   2400   2025 Dorchester RD
Brooklyn   1900   7301 4th AVE
Brooklyn   2000   2071 E 61st ST
Brooklyn   1925   1063 E 2nd ST
Brooklyn   2300   2031 W 6th ST
Brooklyn   2250   9747 Shore RD
Brooklyn   3500   155 Oceana DR
Brooklyn   2759   3510 Neptune AVE
Brooklyn   2200   2832 Bragg ST
Brooklyn   1950   1780 W 3rd ST
Brooklyn   2400   9602 4th AVE
Brooklyn   3500   26 Bay Ridge AVE
Brooklyn   2400   1519 New York AVE
Brooklyn   3304   941 Washington AVE
Brooklyn   3300   412 Herkimer ST
Brooklyn   5203   593 Baltic ST
Brooklyn   7500   78 Amity ST
Brooklyn   2625   692 Chauncey ST
Brooklyn   15000   260 Park AVE
Brooklyn   8750   100 Jay ST
Brooklyn   6455   475 Clermont AVE
Brooklyn   5775   300 Ashland PL

Question Set 2: Two Independent Means Answer the following questions using the NYC2br.MTW file. You can find this dataset in this assignment in Canvas (i.e., where you downloaded this document and where you’ll upload your completed lab). Data were collected from a random sample of two-bedroom apartments posted on Apartments.com in Manhattan and Brooklyn.

A. What is one type of graph that could be used to compare the monthly rental rates of these two-bedroom apartments in Manhattan and Brooklyn? Explain why this is an appropriate graph. [10 points]

B. Using Minitab Express, Construct the graph you described in part A to compare the Manhattan and Brooklyn apartments in this sample. [10 points]

C. Use the five-step hypothesis testing procedure given below to determine if the mean monthly rental rates are different in the populations of all Manhattan and Brooklyn two-bedroom apartments. If assumptions are met, use a t distribution to approximate the sampling distribution. You should not need to do any hand calculations. Use Minitab Express and remember to include all relevant output. [30 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide to reject or fail to reject the null hypothesis

Step 5: State a real-world conclusion

NYC2br.MTW file. - Data Set

Area Rent Address

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. ANOVA table Source SS df MS F Regression 1,870.5782 1 1,870.5782 41.39 Residual 1,265.4934 28 45.1962 Total 3,136.0716 29 Regression output Variables Coefficients Std. Error t(df=28) Intercept 13.7601 3.106 2.914 Distance–X 3.7708 0.5861 6.43 Click here for the Excel Data File 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? How much damage would you estimate for a fire 4 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.

You and your friends have decided to take a trip after the semester ends to celebrate getting through your statistics class. Pick a departure point from a location that is close to your hometown (Denver, CO). You will find a list of ten different destinations for your trip below. ). So, you should have data for 12 different destination points. You need to collect some data online to find the distance between cities as well as the cost of airfare. You do not need to factor in driving distance or cost to get to your departure point – only include the flight distance and cost of airfare between your departure point and each destination.

1. Create a fitted line plot showing the relationship between distance and cost. Based on your plot, how do you think the cost of the trip is associated with the distance of the trip? Why do you think that a perfect linear relationship does not exist? (i.e. why are the points scattered?)

2. Determine the correlation coefficient, r. Interpret this value in the context of the problem. Based on this value, do you think the linear model is a good fit? Why or why not?

3. Interpret the slope and y-intercept of the regression line in the context of the problem.

4. Find residuals

5. Using your regression equation for the line of best fit, predict the cost of flying to each destination based on the distances from your original data. Then calculate the residuals for each data point. Enter this information in a table like shown below.

   1. Destination	Distance (Miles)	Observed Cost	Estimated Cost	Residuals
      Miami, FL	2,066	$755	$207
      San Diego, CA	1,078	$480	$144
      Las Vegas, NV	749	$157	$93
      New York City, NY	1,779	$417	$232
      Honolulu, HI	3,344	$1,600	$714
      Seattle, WA	1,316	$426	$162
      London, England	4,683	$2,225	$842
      Cancun, Mexico	1,670	$544	$368
      Toronto, Canada	1,344	$1,759	$646
      Sydney, Australia	8,325	$1,618	$1,235
      Rome, Italy	5,567	$,1203	$1,313
      -	-	-	-	-

1.You find a quarter in the vending machine at work. Now you have to check the vending machine every day now. This is an example of ___.

2.

Every time you answer a question correctly in class, I praise you. This is an example of which learning theory?

3.

You have a fish tank that contains hundreds of small fish. You feed them the same time everyday by sprinkling the food on the surface of the water. The fish naturally come to the top to feed. One day, not feeding time, you simply check on the fish. As you are standing near the tank, the fish come to the top as though they are feeding. You could say that the fish ___.

4.

You are late for work and you are driving at least 100 miles per hour on the interstate. You are stopped by a State Trooper, and receive a speeding ticket. This is an example of ___.

5.

You go to the circus and see the tiger show. When the trainer cracks his whip, the tiger jumps through the hoop. This is an example of ___.

6.

Most mornings, Randy listens to his favorite song as he gets ready for work, including putting in his contacts. One afternoon, Randy hears his favorite song playing, and his eyes start watering.... something that usually happens only when he puts his contacts in. This is an example of classical conditioning. What is the unconditioned stimulus?

Confidence Intervals for a proportion and mean Do all steps in the confidence interval:

a) Check when easy the requirements for the interval (t-interval)

b) Create a summary of the information that goes into the interval

c) Write out the formula for the interval

d) Replace the symbols in the formula with the numbers from (b)

e) Produce the interval

f) Interpret the interval

In 1998, as an advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of cookies contained at least 1000 chocolate chips. Students tested this by getting bags and counting. Create a 95% interval for the mean number of chocolate chips per bag.

An insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel in 91 of them. Create a 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.

A company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26 miles per gallon. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and a standard deviation of 4.83 mpg. Produce a 99% confidence interval for the average mpg.

A May 2007 Gallup Poll found that only 11% of a random sample of 1003 adults approved of attemps to clone a human. Produce a 90% confidence interval for the percentage of adults that approve of attempts to clone a human

The mayor of a small city suggested that the state locate a new prison there, arguing that the construction project and resulting jobs will be good for the local economy. A total of 2183 residents show up for a public hearing on the proposal, and a show of hands finds only 31 in favor of the prison project. What can the city council conclude about public support for the mayor's initiative? Produce a 98% confidence interval to answer the question.

Understanding the marketplace is the first step to developing and implementing a company’s effective marketing strategy. Consider today’s marketplace, which is crowded with a variety of products and services in all industries. Companies sell their products and services in-store and online as well as offering a hybrid of options to order online and pick up in store. These options are often designed to move the company and its brands to the top place in the industry.

For this discussion, explore the electric and hybrid car industry. Because more emphasis is being placed on sustainable and green technologies for cleaner air and lower gas emissions, customers are becoming more interested in alternative-fuel cars such as hybrids, solar, and electric choices. In addition, as gasoline prices continue to rise for all-fuel automobiles, customers are often looking for more fuel-efficient options to lower their personal expenditure and more.

1. Identify the product’s competition. What is 1 new trend on the horizon that the company needs to consider when offering these models to customers in the future?  

2. Discuss how your selected model is poised to compete in today's marketplace.

3. What type of customer would be interested in your product? Note the demographics such as the age of the consumer, lifestyle, or psychographics. For example, a customer who is a salesperson and travels 200 miles per day might be very interested in this type of car.

The following information is provided to help with your assignment:

Today's marketplace is complex, crowded, and competitive with hundreds of thousands of products and services.

Marketers need to understand that economic value includes market research and industry analysis, both focused on how a product or service matches the wants and needs of the targeted customer. Marketing research about the environment, competition, and customers is critical to company success and creating brand loyalty and awareness.

In analyzing a product or service industry, marketing tools such as a SWOT analysis, which examines the strengths, weaknesses, opportunities, and threats of an organization; a PEST analysis, which focuses on the political, economic, social, and technological sectors of the market; and, Porter’s Five Forces analysis allow marketers to get a top-line and in-depth view of how the brand is situated in the marketplace against the competition, what opportunities and threats exist, and how customers perceive the product.

Case 7

There has been a car accident and the driver if the car was brought to PRU. She has been stabilized in the emergency department; however, transferring her to another facility 40 miles to ICU away would not be appropriate in her health status for her injuries would not sustain life.

The patient has to be placed in ICU in the next 1-2 hours. The night supervisory gains composure and describes the status of patients occupying the 4 ICU beds.

Patient A- A 59 year old female, comatose, stroke victim who had been in ICU for 33 days; uncertain prognosis; retired, with no family

Patient B- 2- week old premature male, has Down's syndrome and has been in ICU since birth; hospital has brought a legal action to permit surgery to repair a duodenal atresia, a procedure the parents had not permitted; family in adjacent city.

Patient C- 35 year old male who underwent emergency appendectomy, developed severe wound infection and septicemia, source of infection is unknown; because of previous anaphylactic shock in reaction to antibiotics; requires ICU care; bachelor; aged mother in city.

Patient D- 13 year old female undergoing chemotherapy for leukemia with an experimental drug; has been in remission three times in the past; close monitoring of the experimental protocol and potential reaction to drug requires ICU care; family in city.
New Patient- 24 year old patient; college honor student in physics. scholarship winner; pregnant; engaged; no family known.

The supervisor ended the brief description by asking, "What should I do?"

You are the superviser and you have to make a decision. (continued on next page) - each question followed must be answered.

Describe your facility

Describe your staff

Explain any legal or ethical issues of the situation

Explain your management style/theory

Discuss cultural issues that the situation presents

Explain budgetary plans or concerns

Explain credentialing or accreditation issues the situation presents

Describe your response to the situation

Exercise 13-60 (LO13-2, LO13-3, LO13-5)

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. How much damage would you estimate for a fire 4 miles from the nearest fire station? (Round your answer to the nearest dollar amount.) [THE ANSWER IS NOT 35]

Exercise 13-58 (LO13-2, LO13-3)

A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results.

1. Which heater looks like the “best buy” based on the size of the residual? (Round residual value to 3 decimal places.)