R has a number of datasets built in. One such dataset is called mtcars. This data set contains fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973-74 models) as reported in a 1974 issue of Motor Trend Magazine.

We do not have to read in these built-in datasets. We can just attach the variables by using the code

        attach(mtcars)

We can just type in mtcars and see the entire dataset. We can see the variable names by using the command

The variables are defined as follows:

mpg Miles/(US) gallon

cyl Number of cylinders

disp Displacement (cu.in.)

hp Gross horsepower

drat Rear

axle ratio

wt Weight (lb/1000)

qsec 1/4 mile time

vs V/S (“V” engine or “Straight line”) (0 or V, 1 for S)

am Transmission (0 = automatic, 1 = manual)
gear Number of forward gears
carb Number of carburetors

We want to model mpg by some or all of the other 10 variables . Do a complete regression analysis. Be sure to comment for each thing you do.

Suppose a prototype for a car was in development. This car has 6 cylinders, 250 cubic in. engine, 130 horsepower, a rear axle ratio of 3.8, weighs 2750 pounds, has a 1/4 mile time of 15.9 seconds, is a V engine type, has automatic transmission, 5 forward gears, and 6 carburetors. With 90% confidence, what is an interval estimate for the predicted mpg for this car?

1. Researchers have long suspected that texting has a detrimental effect on driving behavior. To avoid unnecessary high risk of driving on the roads, driving behavior is measured via driving simulator and the number of mistakes is recorded while texting and not texting as the person is driving the simulator. Mistakes such as failing to stay within the lane, driving at least 10 miles below or above the speed limit, and failing to use the turn signal are automatically recorded. To avoid individual differences in driving behavior, participants are tested twice: once under the “texting while driving” condition and once under the “driving without texting” condition. There are nine participants in the study. Their driving mistakes are reported in the table below.

Question: Do the data support the claim that texting has a detrimental (negative) effect on driving behavior, using an α = 0.05?

For this question, you must follow the steps of hypothesis testing and complete all your calculations by hand. Remember to show your calculations and provide your conclusions in sentence format.

Once you finish this part of the assignment, you can scan or take a photo of your work and paste the scan/photo in your Word document.

Table 1.

Number of mistakes by study participants while using the driving simulator

1.Joe is the owner of a large farm, and Joe wants to be certain that his farm will continue to be used for agricultural purposes after his death. Since none of Joe’s children are interested in maintaining the farm, Joe decides to sell his farm to Lou on condition that Lou uses the farm for agricultural purposes. If Lou fails to do so, ownership of the farm will instantly transfer to a charitable organization called the Farming Preservation Society. What is (or could be) the wording of the granting clause found in the deed that transfers ownership of the farm from Joe to Lou.

2.Eli is the owner of a small commercial farm located in Washington (the state). For the past twenty years, Eli’s farm has relied on water drawn from a lake located three miles away. Each day, Eli (or one of Eli’s employees) would take a truck to the lake and fill-up large tanks with its water. The water would then be driven back to the farm to be used to water the crops. One day, a developer bought a large plot of land adjacent to the lake. This developer intends to construct fifty luxury homes on this plot of land, and they plan to draw water from the lake to fillup the dozens of new swimming pools that will soon be constructed. As a result, there will not be enough water in the lake for Eli to use for his farm. If Eli files a lawsuit to limit the amount of water that the developer can draw from the lake, is Eli likely to succeed? Briefly explain your answer. (3 points)

3.What is the easiest and most reliable way to prove someone has title to real estate?

Josh Adams is 76 years old. Josh has always been very active and busy during his life. He was a welder until he retired at age 60. Since then, he has kept busy fishing, hunting, and golfing. In the past 5 years, Josh has realized that his body has begun to age and he had been experiencing some new aches and pains. Josh decided to see his physician to get some answers about what he is experiencing.

1. Josh states that he is no longer able to complete long drives without stopping to use the restroom. He has a 2-hour drive one way out to the woods and is frustrated that he has to stop to use the restroom. What can you tell Josh he is experiencing?
2. Josh is also upset that he does not have the energy to walk the 2 miles to the pond to fish. What can you tell Josh about his energy as he increases with age?
3. Josh also discussed with the physician his inability to see objects clearly at night. What types of things can you explain to Josh about his vision with age?
4. During the visit, the physician notices that Josh cannot understand what the physician is saying. What issues can occur with older adults and their hearing?
5. What psychological changes, associated with aging, should you be prepared to discuss with Josh?
6. What health promotion and risk reduction measures can Josh incorporate to address the common age-related changes?

1. From Statistics and Data Analysis from Elementary to Intermediate by Tamhane and
Dunlop, pg 339. The following table gives the eye color and hair color of 592 students.

Eye Hair Color Row
Color Black Brown Red Blond Total
Brown 68 119 26 7 220
Blue 20 84 17 94 215
Hazel 15 54 14 10 93
Green 5 29 14 16 64
Column Total 108 286 71 127 592

a) What test should we use to test that the eye color and hair color are associated? Give the null
and alternative hypothesis.
b) Conduct the test at α = 0.05. What do you conclude? Give more than reject or fail to reject
H0.

2. The following data is looking at how long it takes to get to work. Let x = commuting
distance (miles) and y = commuting time (minutes)

x 15 16 17 18 19 20
y 42 35 45 42 49 46

a) Give a scatterplot of this data and comment on the direction, form, and strength of this relationship.

b) Determine the least-squares estimate equation for this data set.
c) Give the coefficient of determination, R2, comment on what that means.
d) Give the residual plot based on the least-squares estimate equation.
e) Test if this least-squares estimate equation specify a useful relationship between commuting
distance and commuting time.

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.)