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. Write out the regression equation

2. How much damage would you estimate for a fire 4 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)

3. 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.)

4. Determine the correlation coefficient. (Round your answer to 3 decimal places.)

5. 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.)

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

HYPOTHESIS TESTING SUMMARY ACTIVITY

Part 1: Overview of the Hypothesis Test for the Population Proportion Answer the following questions:

1) The general form of the test statistic for the hypothesis test for a population proportion is shown below. Label the different components of the test statistic.

2) For the following situations, state the null and alternative hypothesis. Then determine whether the alternative hypothesis is one-sided or two-sided.

a) A toy manufacturer claims that 23% of the 14-year-old residents of a certain city own a skateboard. A sample of fifty 14-year-olds shows that nine own a skateboard. Is there enough evidence to show that the percentage has changed?

b) At a large university, a study found that 25% of the students who commute travel more than 14 miles to campus. Recently, the university built more housing closer to campus so they believe that the proportion has decreased.

c) For students who first enrolled in two-year public institutions in fall 2007, the proportion who earned a bachelor’s degree within 6 years was 0.399. The president of Joliet Junior College believes that the proportion of students who enroll in her institution have a higher completion rate.

3) Use the information in question 2a (toy manufacturer) to answer the following questions.

a) Calculate the test statistic and draw a diagram with a normal curve to represent the sampling distribution of ??� in the context of this situation.

b) If the sample size of the survey was increased, would the test statistic increase or decrease? Would it give us more or less evidence against H0 ?

For each measurement listed below replace the “?” with the most appropriate level or scale of measurement: nominal, ordinal, interval, ratio.

An analyst at a local automotive garage wanted to see if there were relationships between repair time in hours (y) and months since last service(x1), type of repair(x2), whether it was a truck or car(x3), or the mileage of the vehicle(x4). Use a level of significance of 0.05.

1. What is the dependent variable?

2. What are the independent variables?

3. Run the regression analysis with the four independent variables. Write out the prediction equation.

4. From a global perspective is the model worth keeping? Why?

5. Evaluate the individual independent variables, circle the variables would you consider removing? Explain why?          X1                         X2                           X3                            X4

6. Rerun the regression analysis after removing the unnecessary independent variables. Write the regression equation:

7. What repair time will it take for a car with 90000 miles, not serviced for six months, and requires for electrical repairs?

A larger and more modern main post office is to be constructed at a new location in​ Davis, California. Growing suburbs caused a shift in the population density from where it was 40 years​ ago, when the current facility was built. Annette​ Werk, the​ postmaster, asked her assistants to draw a grid map of the seven points where mail is picked up and delivered in bulk. The coordinates and trips per day to and from the seven mail source points and the current main post​ office, M, are shown in the following table. M will continue to act as a mail source point after relocation.  

a. Calculate the center of gravity as a possible location for the new facility. ​(Enter your responses rounded to the nearest whole​ number.)

The center of gravity​ "X" coordinate​ =

The center of gravity​ "Y" coordinate​ =

b. Compare the​ load-distance scores for the location in part​ (a) and the current​ location, using rectilinear distance. ​(Round all intermediate calculations to the nearest whole​ number.)

The​ load-distance score to​ "M" is

​ (Enter your response as an​ integer.)

The​ load-distance score to the center of gravity is

​(Enter your response rounded to the nearest whole​ number.)

A project requires a contractor to excavate 28,000 bank CY dry earth, haul it away to a borrow area located 3 miles away. The contractor has 4 weeks to complete the work. The contractor doing the work has decided to mobilize scrapers with a capacity of 20 loose CY. Each Scraper has a typical cycle time of 20 minutes due to the rough terrain at the site. The contractor can purchase one scraper but will have to rent additional scrapers if necessary. The cost data for a CAT 621 Scraper is as follows: A new CAT 621G costs $450,000 (without tires). The contractor plans to use it for five years (average 2000 hours per year) and sell it for $190,000. The scraper tires cost $4,250/tire (scraper has 4 tires) and will likely last 6000 hours. The scraper consumes 10 gallons of fuel per hour. Diesel cost can be estimated at $3.0/gal. The annual maintenance cost for the scraper can be estimated at $18,000. Scraper operator costs $58.00 /hour including overheads. The rate of interest can be assumed to be 6.5%. The rental agency is willing to rent a 621G for $6,000 per week or $ 18,000 per month. The contractor will have to provide fuel and operator. The mobilization and demobilization cost for each scraper is $2,500. Based on this information, analyze the earthwork operations. Make recommendations:

1. How many scrapers should the contractor rent?

2. Estimate the cost in $$/bank CY

(Please show all work clearly and neatly)

1. If you can read at an average rate of 5.15 words per second, how long will it take you to read a 505 page book that has an average of 995 words per page?

2. Let’s say you need to make 12.0 dozen cookies. You decide to make these cookies in batches of 24.0 cookies each. Each batch of cookies requires 27.0 mL of vanilla extract. Each bottle of vanilla extract contains 150. mL of liquid. How many bottles of vanilla extract will you need to make all of your cookies?

3. The label on a bottle of orange juice says that each serving of juice provides you with 480. mg of potassium. The label also says that a serving size is 8.00 fluid ounces and that there are two servings per container. In addition, the label says that 480. mg of potassium is 14.0% of the recommended daily amount of potassium that you ingest in a 2000. calorie diet. How many servings of orange juice do you need to ingest to get 100.% of the recommended daily amount of potassium?

4. My car burns oil at a rate of 1.00 quart every 895 miles. If I travel an average of 83,454 km per year, how many liters of oil do I burn in 11.0 years?

5. If my back yard has an area of 75.5 square zzbts, what is the area in square oobts?

1.00 oobt = 3.43 qvsts

1.00 qvst = 15.4 zzbts

The data below are from a study conducted by a consumer research group on the fuel efficiency (rated based on city miles per gallon) of the 30 top-selling U.S. automobiles.

23 20 16 13 34 27

24 10 16 12 34 26

14 31 15 12 16 36

18 22 15 19 28 38

10 16 14 23 19 44

1. Enter the data into a spreadsheet. Be sure to clearly label and neatly format your spreadsheet.

2. Calculate the sum of these data two different ways: a. By writing your own formula. Clearly label the result. b. By using the SUM spreadsheet function. Clearly label the result

. 3. Use the COUNT function to calculate the N of this sample data set. Clearly label the result.

4. Calculate the arithmetic average (mean) of these data by writing your own formula. Clearly label.

5. Create a new column of data in which you subtract the mean fuel efficiency from each individual fuel efficiency score (i.e., MPG – mean). Be sure to use the proper relative and absolute references (indicated with $ signs) to perform these calculations.

6. Now compute the sum, N, and mean of your new (MPG – mean) scores.

7. Create one more new column of data in which you square each of the (MPG – mean) scores. 8. Finally, compute the sum, N, and mean of your new (MPG – mean)^2 scores