We are interested in exploring the relationship between the weight of a vehicle and its fuel efficiency (gasoline mileage). The data in the table show the weights, in pounds, and fuel efficiency, measured in miles per gallon, for a sample of 12 vehicles.

Find the correlation coefficient.

Find the equation of the best fit line. (Round your answers to four decimal places.)

What percent of the variation in fuel efficiency is explained by the variation in the weight of the vehicles, using the regression line? (Round your answer to the nearest whole number.

For the vehicle that weighs 3000 pounds, find the residual

(y − ŷ).

(Round your answer to two decimal places.)

Remove the outlier from the sample data. Find the new correlation coefficient and coefficient of determination. (Round your answers to two decimal places.)

Ramp metering is a traffic engineering idea that requires cars entering a freeway to stop for a certain period of time before joining the traffic flow. The theory is that ramp metering controls the number of cars on the freeway and the number of cars accessing the​ freeway, resulting in a freer flow of​ cars, which ultimately results in faster travel times. To test whether ramp metering is effective in reducing travel​ times, engineers conducted an experiment in which a section of freeway had ramp meters installed on the​ on-ramps. The response variable for the study was speed of the vehicles. A random sample of 15 cars on the highway for a Monday at 6 p.m. with the ramp meters on and a second random sample of 15 cars on a different Monday at 6 p.m. with the meters off resulted in the following speeds​ (in miles per​ hour).

Ramp_Meters_On   Ramp_Meters_Off
27   24
38   33
43   47
35   29
42   37
47   25
32   36
47   39
56   22
27   51
57   41
26   31
51   17
40   41
46   42

Determine the​ P-value for this test.

​P-value equals=.? ​(Round to three decimal places as​ needed.)

Tiffany is a model rocket enthusiast. She has been working on a pressurized rocket filled with nitrous oxide. According to her design, if the atmospheric pressure exerted on the rocket is less than 10 pounds/sq.in., the nitrous oxide chamber inside the rocket will explode. Tiff worked from a formula p=14.7e−h/10p=14.7e−h/10 pounds/sq.in. for the atmospheric pressure hh miles above sea level. Assume that the rocket is launched at an angle of αα above level ground at sea level with an initial speed of 1400 feet/sec. Also, assume the height (in feet) of the rocket at time tt seconds is given by the equation y(t)=−16t2+1400sin(α)ty(t)=−16t2+1400sin⁡(α)t. [UW]

a. At what altitude will the rocket explode?
b. If the angle of launch is αα = 12∘∘, determine the minimum atmospheric pressure exerted on the rocket during its flight. Will the rocket explode in midair?
c. If the angle of launch is αα = 82∘∘, determine the minimum atmospheric pressure exerted on the rocket during its flight. Will the rocket explode in midair?
d. Find the largest launch angle αα so that the rocket will not explode.

1.)In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 51 and a standard deviation of 4. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 43 and 59?

2.)A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 38 months and a standard deviation of 3 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 41 and 47 months?

3.)he physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 60 and a standard deviation of 8. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 52 and 60?

The accompanying table shows a portion of a data set that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City.

a. Estimate the sample regression equation that enables us to predict property taxes on the basis of the size of the home. (Round your answers to 2 decimal places.)

taxes = ______ + ______ size

b. Interpret the slope coefficient.

a. As Property Taxes increase by 1 dollar, the size of the house increases by 6.78 ft.

b. As Size increases by 1 square foot, the property taxes are predicted to increase by $6.78.

c. Predict the property taxes for a 1,500-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

taxes _________

24)____________       An SAT prep course claims to improve the test scores of students. The

                                     table shows the scores for seven students the first two times they took                    

25)_____________     the verbal SAT. Before taking the SAT for the second time, each

                                     student took a course to try to improve his or her verbal SAT scores.  

                                     Test the claim at a = .05. List the a) null hypothesis b) average difference       

                                   between the scores        

26)______________   In a crash test at five miles per hour, the mean bumper repair cost for 14

                                    midsize cars was $547 with a standard deviation of $85. In a similar test               

                                    of 23 small cars, the mean bumper repair cost was $347 with a standard                      

27)______________ deviation of $185. At a = 0.05, can you conclude that the mean bumper

                                    repair cost is the same for midsize cars and small cars? List the

                                    26) p-value 27) accept or reject.

The accompanying table shows a portion of a data set that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City.

a. Estimate the sample regression equation that enables us to predict property taxes on the basis of the size of the home. (Round your answers to 2 decimal places.)

Taxesˆ = _____ + _____Size.

b. Interpret the slope coefficient.

As Size increases by 1 square foot, the property taxes are predicted to increase by $6.85.

As Property Taxes increase by 1 dollar, the size of the house increases by 6.85 ft.

c. Predict the property taxes for a 1,200-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) Taxesˆ

A used car dealer wants to develop a regression equation that determines mileage as a function of the age of a car in years. He collects the data shown below for the 12 cars he has on his lot.

a) What is the slope of the regression equation? Give your answer to two decimal places.  
b) What is the value of the correlation coefficient? Give your answer to two decimal places.  
c) A 4 year old car is delivered to his lot with 160000 miles. Manually enter these values in the data table above and rerun the regression analysis. What is the value of the slope? Give your answer to two decimal places.  
d) Including the additional car, what is the value of the correlation coefficient? Give your answer to two decimal places.  
e) Did the additional car strengthen or weaken the linear relationship between age and mileage?

It strengthened the linear relationship.

It weakened the linear relationship.

   Can not be determined.

A 26-year-old male prisoner begins a hunger strike to protest what he considers unfair prison policies. He drinks only tap water, and his only exercise is two daily half-hour walks at approximately 2.5 miles/hr. The temperature in his cell is maintained at 220C. His starting weight is 70 Kg, of which 14% is body fat. At the end of 4 weeks, he is urged by the prison physician, family, friends, and his attorney to stop his fast because of his deteriorating conditions.

a. What changes in plasma levels of energy substrates would occur in the first 3 days of his fast?

b. On what immediate and on what ultimate sources of energy would brain metabolism depend?

c. What role would the liver play in providing energy sources to the brain and muscles?

d. What early changes in plasma levels of hormones would occur? How would this regulate his energy metabolism?

e. What physiologic events would occur when he stopped his fast by drinking a large quantity of a high glucose fluid?