Mr. and Mrs. Roberts checked into the Acme Hotel Downtown. Mr. Roberts gave his car keys to the hotel valet so that the valet could park the car and retrieve the car when it was needed. A sign adjacent to the valet stand advises that valet parking is $30 per night and that the hotel is not responsible for damage or loss vehicles. When Mr. Roberts requests the valet deliver his car the following day, the car is missing. Briefly discuss the legal relationship, if any, between the hotel and Mr. Roberts with respect to his vehicle.

What, if any, effect does the disclaimer on the garage sign?

The Toyota Camry is one of the best-selling cars in North America. The cost of a previously owned Camry depends on many factors, including the model year, mileage, and condition. To investigate the relationship between the car’s mileage and the sales price for Camrys, the following data show the mileage and sale price for 19 sales (PriceHub web site, February 24, 2012).

DATA

Miles (1,000s) Price ($1,000s) 22 16.2 29 16.0 36 13.8 47 11.5 63 12.5 77 12.9 73 11.2 87 13.0 92 11.8 101 10.8 110 8.3 28 12.5 59 11.1 68 15.0 68 12.2 91 13.0 42 15.6 65 12.7 110 8.3

(a) Choose a scatter chart below with ‘Miles (1000s)’ as the independent variable. (i) (ii) (iii) (iv) What does the scatter chart indicate about the relationship between price and miles? The scatter chart indicates there may be a linear relationship between miles and price. Since a Camry with higher miles will generally sell for a lower price, a negative relationship is expected between these two variables. This scatter chart is consistent with what is expected.

(b) Develop an estimated regression equation showing how price is related to miles. What is the estimated regression model? Let x represent the miles. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) = + x

(c) Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.01 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(d) How much of the variation in the sample values of price does the model estimated in part (b) explain? If required, round your answer to two decimal places. %

(e) For the model estimated in part (b), calculate the predicted price and residual for each automobile in the data. Identify the two automobiles that were the biggest bargains. If required, round your answer to the nearest whole number. The best bargain is the Camry # in the data set, which has miles, and sells for $ less than its predicted price. The second best bargain is the Camry # in the data set, which has miles, and sells for $ less than its predicted price.

(f) Suppose that you are considering purchasing a previously owned Camry that has been driven 100,000 miles. Use the estimated regression equation developed in part (b) to predict the price for this car. If required, round your answer to one decimal place. Do not round intermediate calculations. Predicted price: $ Is this the price you would offer the seller?

Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Write code to ask user to provide input length in miles, yards, feet and inches and write code to convert sum of total length into meters. Display result by reiterating input values in inches, feet, yards, and miles entered by user, and the sum of the total length in meters. PLEASE use bluej for code

Use this data for Questions 20-24

The distance travelled (in hundreds of miles) and sales (in thousands of dollars) for ACME Company are reflected in table below:

1. What is the Coefficient of Determination?
   1. 0.7334
   2. 0.4053
   3. 0.2267
   4. 0.1437

2. What is the Test Statistic for the Correlation Coefficient?
   1. 3.32
   2. 16.15
   3. 1.88
   4. Cannot be computed

3. What is the regression slope?
   1. 1.98
   2. 0.40
   3. 0.71
   4. 0.32

4. What is the regression intercept?
   1. 0.40
   2. 2.41
   3. 3.68
   4. 1.88
5. If a salesman travels 600 miles what is the predicted sales?
   1. $4826
   2. $2105
   3. $3638
   4. $4018

Show all work.

Computers in some vehicles calculate various quantities related to performance. One of these is fuel efficiency, or gas mileage, usually expresses as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank filled, and the computer was then reset. Here are the mpg values for a random sample of 20 of these records: 41.5 50.7 36.6 37.3 34.2 45.0 48.0 43.2 47.7 42.2 43.2 44.6 48.4 46.4 46.8 39.9 37.3 43.5 44.3 43.3 Find a 95% confidence interval for μ, the mean miles per gallon for this vehicle.

Create a flowchart for the following:

Mr. Arthur Einstein, your college physics teacher, wants a program for English-to-Metric conversions. The program should be able to convert from kilometers to miles, kilograms to pounds, and liters to quarts. The program should first determine the type of conversion desired. To do this, the user will enter a letter indicating the type of measurement: pounds (P), miles (M), and quarts (Q). After doing this, the program should proceed to read the appropriate metric value and convert it to the correct imperial value. Use the following conversion factors:

1 kilometer = 0.621388 miles

1 kilogram = 2.2046 pounds

1 liter = 0.877193 quarts

A boat leaves the harbor entrance and travels 27 miles in the direction ??? ° ?. The captain then travels for another 16 miles in the direction ??? ° ?, which is the boat’s final position. How far is the harbor entrance from the boat’s final position? What is the bearing of the boat from the harbor entrance? Round your answers to the nearest WHOLE numbers.

Two airplanes are flying in the air at the same height. Airplane A is flying east at 250 mph and airplane B is flying north at 400 mph. If they are both heading to the same airport, located 30 miles east of airplane A and 40 miles north of airplane B, at what rate (in mph) is the distance between the airplanes changing?

In a random sample of five people, the mean driving distance to work was 25.4 miles and the standard deviation was 5.2 miles. Assume the random variable is normally distributed and use a t-distribution to find the margin of error and construct confidence intervals for the population mean at the following confidence levels:

a. 85%

b. 90%

c. 99%

An engineer wants to determine how the weight of a​ gas-powered car,​ x, affects gas​ mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts​ (a) through​ (d) below.

Weight (pounds), x   Miles per Gallon, y
3736 17
3938 17
2746 24
3485 19
3250 22
3035 24
3826 16
2506 23
3387 18
3847 18
3251 17

​(a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.

y^= (BLANK, round to 5 decimal places as needed)x + (BLANK, round to two decimal places as needed)

​(b) Interpret the slope and​ y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice.(Use answer from part A to find this answer)

A. A weightless car will get (BLANK) miles per​ gallon, on average. It is not appropriate to interpret the slope.

B. For every pound added to the weight of the​ car, gas mileage in the city will decrease by (BLANK) ​mile(s) per​ gallon, on average. A weightless car will get (BLANK)

miles per​ gallon, on average.

C. For every pound added to the weight of the​ car, gas mileage in the city will decrease by (BLANK) ​mile(s) per​ gallon, on average. It is not appropriate to interpret the​ y-intercept.

D. It is not appropriate to interpret the slope or the​ y-intercept.

​(c) A certain​ gas-powered car weighs 3700 pounds and gets 20 miles per gallon. Is the miles per gallon of this car above average or below average for cars of this​ weight?

A. Above

B. Below

​(d) Would it be reasonable to use the​ least-squares regression line to predict the miles per gallon of a hybrid gas and electric​ car? Why or why​ not?

A.​ No, because the absolute value of the correlation coefficient is less than the critical value for a sample size of n =11.

B.​Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n =11.

C. ​No, because the hybrid is a different type of car.

D. ​Yes, because the hybrid is partially powered by gas.