19) -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   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? a) List the p-value b) accept or reject.

- Last year the average daily change in the Dow Jones Industrial Index was 7.3 points. A random sample of 15 trading days this year showed the average change to be 5.6 points with standard deviation 10.2. Test the claim that the average change in the index is less this year than it was last year. a) List the p-value b) Have we proven that the change is significant? (yes or no) c) what type of error could be made with the type of conclusion drawn from the results of this study?

Currently, a manager is using a regression model that predicts gas mileage​ (in miles per​ gallon) based on the horsepower of a car and the​ car's weight​ (in pounds). She believes that the effect of HP on gas milage is affected by the weight and vice versa. Develop a regression model that includes​ horsepower, weight, and this new interaction effect to predict gas mileage. Complete parts​ (a) and​ (b).

MPG- 15.3,19.5,20.8,18.9,17.2,27.5,44.4,27.2,28.3,21.1

Horsepower-187,101,143,171,166,72,70,89,87,134

Weight-4757,3537,3227,4448,4296,3191,2106,2490,2605,3871

a. At the 0.01level of​ significance, is there evidence that the interaction term makes a significant contribution to the​ model?

Let the interaction variable be X3.

What are the null and alternative hypotheses for this​ test?

A.H0​:β3=0

H1​:β3>0

B.H0​:β3≥0

H1​:β3<0

C.H0​:β3≠0

H1​:β3=0

D.H0​:β3≤0

H1​:β3>0

E.H0​:β3=0

H1​:β3≠0

F.H0​:β3=0

H1​:β3<0

What is the​ p-value for this​ test?

​p-value=

​(Round to three decimal places as​ needed.)

What is the conclusion for this​ test?

Since the​ p-value for the interaction term is ___than α​,____H0.

There____ enough evidence to conclude that the interaction term makes a significant contribution to the model.

b. Which regression model is more​appropriate, the original given model or the new model with the interaction​ term? Explain.

A.The new model is more appropriate because the interaction is not significant.

B.The new model is more appropriate because the interaction is significant.

C.The old model is more appropriate because the interaction is not significant.

D.The old model is more appropriate because the interaction is significant.

E.The new model is more appropriate because the coefficient of the interaction term is not equal to 0.

3)The data provided give the gasoline mileage​ (in miles per​ gallon) based on the horsepower of a​ car's engine and the weight of the car​ (in pounds). Using the data​ provided, determine the VIF for each independent variable in the model. Is there reason to suspect the existence of​ collinearity?

MPG- 15.3,19.9,20.5,18.4,17.5,27.2,44.8,27.9,28.4,21.2

Horsepower- 191,108,140,173,164,68,60,85,85,135

weight- 4724,3531,3223,4494,4297,3192,2111,2487,2606,3874

Determine the VIF for each independent variable in the model.

VIF 1=___

VIF 2=___

​(Round to three decimal places as​ needed.)

Is there reason to suspect the existence of ​collinearity?

A.Yes. The VIF for each independent variable is less than 5.

B.No. The VIF for each independent variable is greater than 5.

C.Yes. The VIF for each independent variable is greater than 5.

D.No. The VIF for each independent variable is less than 5.

Suppose the distances​ (in miles) that a pharmaceutical​ representative, Tracy​ Ross, travels between medical offices are shown in the accompanying table. Set up and solve a traveling salesperson problem using Evolutionary Solver.

The shortest distance for a tour is _____ miles?

To

From      1             2              3              4              5              6              7              8             

1              0              3              57           51           49           4              12           92

2              3              0              51           10           53           25           80           53

3              57           51           0              49           18           30           6              47

4              51           10           49           0              50           11           91           38

5              49           53           18           50           0              38           62           9                             

6              4              25           30           11           68           0              48           94

7              12           80           6              91           62           48           0              9

8              92           53           47           38           9              94           9              0

Ben Paul is an accounting major at a western university located approximately 60 miles from a major city. Many of the students attending the university are from the metropolitan area and visit their homes regularly on the weekends. Ben, an entrepreneur at heart, realizes that few good commuting alternatives are available for students doing weekend travel. He believes that a weekend commuting service could be organized and run profitably from several suburban and downtown shopping mall locations. Ben has gathered the following investment information.

1.         Five used vans would cost a total of $90,000 to purchase and would have a 3-year useful life

    with negligible salvage value. Ben plans to use straight-line depreciation.

2.         Ten drivers would have to be employed at a total payroll expense of $43,000.

3.         Other annual out-of-pocket expenses associated with running the commuter service would  

    include Gasoline $26,000, Maintenance $4,000, Repairs $5,300, Insurance $4,500,

    Advertising $2,200.

4.         Ben desires to earn a return of 15% on his investment.

5.         Ben expects each van to make ten round trips weekly and carry an average of six students

    each trip. The service is expected to operate 32 weeks each year, and each student will be

    charged $15 for a round-trip ticket.

Instructions

(a)         Determine the annual:

                                                           (1) net income and

           (2) net annual cash flows for the commuter service.

(b)       Compute the:

           (1) cash payback period and

           (2) annual rate of return. (Round to two decimals.)

(c)         Compute the net present value of the commuter service. (Round to nearest dollar.)

(d)         What should Ben conclude from these computations?

The following data give the odometer mileage (rounded to the nearest thousand miles) for all 20 cars that are for sale at a dealership.

a. Calculate the values of the three quartiles and the interquartile range.

Q₁ =

Q₂ =

Q₃ =

IQR =

b. Find the approximate value of the 19^th percentile.

c. Calculate the percentile rank of 71.

%

3. The following frequency table summarizes the distances in miles of 120 patients from a regional hospital. Distance Frequency 0-4 40 4-8 30 8-12 20 12-16 20 16-20 10 Calculate the sample variance and standard deviation for this data (since it is a case of grouped data- use group or class midpoints in the formula in place of X values, and first calculate the sample mean).

Overall, the Miles Per Gallon for customers of MallState is normally distributed around 34 MPG with a standard deviation of 2.5 MPG.

In looking to reward environmentally friendly drivers, the insurer decides to reward drivers whose cars rank in the top 10%ile of MPG. What is the top 10%ile and which guest(s) from problem G would benefit from this program?

The following frequency table summarizes the distances in miles of 100 patients from a regional hospital.

Distance Frequency

0-4 20

4-8 25

4-12 30

12-16 20

16-24 5

Calculate the sample variance and standard deviation for this data (since it is a case of grouped data- use group or class midpoints in the formula in place of X values, and first calculate the sample mean)

Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 31.6 and 4.9 mpg, respectively.

a. What is the probability that a randomly selected passenger car gets more than 35 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

b. What is the probability that the average mpg of two randomly selected passenger cars is more than 35 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. If two passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 35 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 35.9 and 2.5 mpg, respectively. [You may find it useful to reference the z table.]

a. What is the probability that a randomly selected passenger car gets more than 37 mpg?

b. What is the probability that the average mpg of three randomly selected passenger cars is more than 37 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. If three passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 37 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)