According to a recent government survey, the daily one-way commuting distance
of U. S. workers averages 13 miles. An investigator wishes to determine whether the
national average describes the mean commute distance for all workers in the Chicago area.
Commute distances are obtained for a random sample of 100 workers from this area, and the
mean distance is found to be 12.25 miles with a standard deviation of 2.5 miles. Test the null
hypothesis at the .05 level of significance.

A. State H 0 : ______________________
B. State H A : ______________________
C. Is this a one- or two-tail test? Why? ______________________________________
D. What is(are) the critical value(s)? ______________________
E. What is the decision rule? _______________________________________________
F. Calculate the t statistic:

t = x̄- µm/ s/√n

G. What is your decision regarding H 0 and why? _______________________________
H. Interpretation of the results: _____________________________________________

Moana (an expert sailor) is sailing from her home to a nearby island which is 125 miles north and 125 miles west. There is a constant ocean current of 0.50 knots (kn) moving from west to east. Moana can sail her boat at a cruising speed of 5.5 miles per hour in still water.

1. What angle should Moana sail to get to the island?

2. How long will it take her to get there?

3. Moana’s friend Maui is floating on a raft that is moving with the ocean current (meaning, he is not traveling with respect to the water). Would Maui see Moana’s boat traveling with a speed faster than, slower than, or equal to what an observer standing on the shore would see? Explain your reasoning

Answer all questions. Show all of your work. Turn in all relevant computer STATA printouts.

Problem 1 (20 points). Show work

Consider the following regression on the average miles per gallon achieved by a random sample of 500 automobiles:

            MPGi = 20.4 + 2.5 FOREIGNi – 3.1 WEIGHTi + 1.2 (FOREIGNi*WEIGHTi)

Where:

MPGi is the average miles per gallon achieved by the ith car

FOREIGNi is a dummy variable equal to 1 if the ith car is made outside the United States, zero otherwise.

WEIGHTi is the weight of the ith car, in thousands of pounds.

FOREIGNi*WEIGHTi is the interaction between FOREIGN and WEIGHT

a.   Interpret the meaning of the coefficient on FOREIGN*WEIGHT.

      b.   If the weight of a foreign car increases 3000 pounds, what is the change in miles per gallon?

Suppose that you are interested in estimating the average number of miles per gallon of gasoline your car can get. You calculate the miles per gallon for each of the next twenty-five times you fill the tank. Suppose that in truth, the values for your car are bell-shaped, with a mean of 20 miles per gallon and a standard deviation of 1. Find the possible sample means you are likely to get based on your sample of twenty-five observations. Consider the intervals into which 68%, 95%, and almost all of the potential sample means will fall, using the Empirical Rule. (Round all answers to the nearest thousandth.)

About 68% of possible sample means will be in the range between ___ and ____ .

About 95% of possible sample means will be in the range between ____ and ____ .

About 99.7% of possible sample means will be in the range between ____ and ____.

1. A freeway has the following characteristics:
   • 6 lanes, 3 in each direction
   • 13’ lanes
   • 8’ right side lateral clearance
   • Total of 4 ramps in the 3 miles upstream and 3 miles downstream of the midpoint of the facility
   • 2% upgrade for 1.5 miles
   • Urban facility with 50% delivery trucks and 50% freight trucks
   • 8% trucks
   • 3,400 veh/hr in the analysis direction in the peak hour
   • 955 vehicles in the peak 15-minute time period

1. (3)  What is the free flow speed of the facility?

2. (3)  What is the passenger car equivalent flow rate?

3. (3)  What is the estimated operating speed of the facility?

4. (2)  What is the density of the facility?

5. (2)  What is the LOS of the facility?

6. (2)  Describe what the LOS indicates about how well the facility is operating?

Write a C ++ program that asks the user for the speed of a vehicle (in miles per hour) and how many hours it has traveled. The program should then use a loop to display the distance the vehicle has traveled for each hour of that time period. Here is an example of the output:

What is the speed of the vehicle in mph? 40
How many hours has it traveled? 3
Hour Distance Traveled
--------------------------------
1           40
2           80
3          120

Input Validation: Do not accept a negative number for speed and do not accept any value less than 1 for time traveled.

Distance Traveled

The distance a vehicle travels can be calculated as follows:

   distance = speed * time

For example, if a train travels 40 miles per hour for 3 hours, the distance traveled is 120 miles.

Introduce variables to represent items of interest in the problem. For

example, (1) Let n be the number to be found, or (2) Let a be Alice’s

current age, or (3) Let r be the rate of the first car.

(2)

Write down an equation using the information given in the problem. This

is the really important part for this particular assignment!

(3)

Solve the equation and find the value requested in the problem.

The distance between A and B is 180 miles. An automobile at A starts for B are the rate of 40 miles per hour at the same time that an automobile at B starts for A at the rate of 50 miles per

hour. How long will it be before the automobiles meet?

A snail leaves A and travels at the rate of four inches per minute to B. At B the snail catches a ride on a turtle and is carried back the A at the rate of ten inches per minute. If the round trip takes 14 minutes, what is the distance between A and B?

Two boats start at the same point, one goes straight north, the

other straight south. The first boat travels twice as fast as the

second. After three hours they are 72 miles apart. Find the rate

of the faster boat.

Intro C++ Programming Chapter 6 Functions

You have been tasked to write a new program for the Research Center's shipping department. The shipping charges for the center are as follows:

Weight of Package (in kilograms)                Rate per mile Shipped
2 kg or less                                                      $0.05
Over 2 kg but no more than 6 kg    $0.09
Over 6 kg but not more than 10 kg    $0.12
Over 10 kg    $0.20

Write a function in a program that asks for the weight of a package in kilograms and the distance it is to be shipped. Using that data, write another function that calculates the shipping charge and returns it to the main program and displays the value there.

For the second function, pass the two values (weight and distance) into the function as arguments. In the function if the shipping distance the user provided earlier is a distance greater than 200 miles, there will be an additional charge of $25 added to the order. For example, if an item weighing 20 kg is shipped 250 miles, the total cost will be $75, calculated by the formula: ((250 miles * 0.20) + 25).

input validation: Do not accept any weights less than 0.5 kilograms, nor any distances less than 0 miles.

Your small remodeling business has two work vehicles. One is a small passenger car used for job site visits and for other general business purposes. The other is a heavy truck used to haul equipment. The car gets 25 miles per gallon (mpg). The truck gets 10 mpg. You want to improve gas mileage to save money, and you have enough money to upgrade one vehicle. The upgrade cost will be the same for both vehicles. An upgraded car will get 40 mpg; an upgraded truck will get 12.5 mpg. The cost of gasoline is $2.65 per gallon. Calculate the annual fuel savings in gallons for the truck and car assuming both vehicles are driven 12,000 miles per year. (Do not round intermediate calculations.) Assuming an upgrade is a good idea in the first place, which one should you upgrade? Both vehicles are driven 12,000 miles per year.

Truck Gallons per year=

Car Gallons per year=