1. In a survey, 20 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $43.1 and standard deviation of $9.4. Construct a confidence interval at a 90% confidence level.

Express your answer in the format of ¯xx¯ ±± Error.

$ ±± $

2. The body temperatures in degrees Fahrenheit of a sample of 5 adults in one small town are:

Assume body temperatures of adults are normally distributed. Based on this data, find the 80% confidence interval of the mean body temperature of adults in the town. Enter your answer as an open-interval (i.e., parentheses) accurate to twp decimal places (because the sample data are reported accurate to one decimal place).

80% C.I. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

3.

The body temperatures in degrees Fahrenheit of a sample of adults in one small town are:

Assume body temperatures of adults are normally distributed. Based on this data, find the 98% confidence interval of the mean body temperature of adults in the town. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.

98% C.I. =    

4.

You are interested in finding a 90% confidence interval for the average commute that non-residential students have to their college. The data below show the number of commute miles for 14 randomly selected non-residential college students.

a. To compute the confidence interval use a ? t z  distribution.

b. With 90% confidence the population mean commute for non-residential college students is between  and   miles.

c. If many groups of 14 randomly selected non-residential college students are surveyed, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population mean number of commute miles and about  percent will not contain the true population mean number of commute miles.

5.

A psychiatrist is interested in finding a 90% confidence interval for the tics per hour exhibited by children with Tourette syndrome. The data below show the tics in an observed hour for 15 randomly selected children with Tourette syndrome. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? t z  distribution.

b. With 90% confidence the population mean number of tics per hour that children with Tourette syndrome exhibit is between  and .

c. If many groups of 15 randomly selected children with Tourette syndrome are observed, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population mean number of tics per hour and about  percent will not contain the true population mean number of tics per hour.

6.

You are interested in finding a 90% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 13 randomly selected physical therapy patients.

a. To compute the confidence interval use a ? t z  distribution.

b. With 90% confidence the population mean number of visits per physical therapy patient is between  and   visits.

c. If many groups of 13 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population mean number of visits per patient and about  percent will not contain the true population mean number of visits per patient.

1. Define a class called Odometer that will be used to track fuel and mileage for an automobile. The class should have instance variables to track the miles driven and the fuel efficiency of the vehicle in miles per gallon. Include a mutator method to reset the odometer to zero miles, a mutator method to set the fuel efficiency, a mutator method that accepts miles driven for a trip and adds it to the odometer’s total, and an accessor method that returns the number of gallons of gasoline that the vehicle has consumed since the odometer was last reset.

Use your class with a test program that creates several trips with different fuel efficiencies. You should decide which variables should be public, if any.

2. Write a grading program for a class with the following grading policies:

1. There are three quizzes, each graded on the basis of 10 points.

2. There is one miterm exm, graded on the basis of 100 points.

3. There is one finl exm, graded on the basis of 100 points.

The fnal exm counts for 40% of the grade. The miterm counts for 35% of the grade. The three quizzes together count for a total of 25% of the grade. (Do not forget to convert the quiz scores to percentages before they are averaged in.)

Any grade of 90 or more is an A, any grade of 80 or more (but less than 90) is a B, any grade of 70 or more (but less than 80) is a C, any grade of 60 or more (but less than 70) is a D, and any grade below 60 is an F. The program should read in the student’s scores and output the student’s record, which consists of three quiz scores and two exm scores, as well as the student’s overall numeric score for the entire course and final letter grade.

Define and use a class for the student record. The class should have instance variables for the quizzes, midterm, final, overall numeric score for the course, and final letter grade. The overall numeric score is a number in the range 0 to 100, which represents the weighted average of the student’s work. The class should have methods to compute the overall numeric grade and the final letter grade. These last methods should be void methods that set the appropriate instance variables. Your class should have a reasonable set of accessor and mutator methods, an equals method, and a toString method, whether or not your program uses them. You may add other methods if you wish.

3. Write a Temperature class that has two instance variables: a temperature value (a floating-point number) and a character for the scale, either C for Celsius or F for Fahrenheit. The class should have four constructor methods: one for each instance variable (assume zero degrees if no value is specified and Celsius if no scale is specified), one with two parameters for the two instance variables, and a no-argument constructor (set to zero degrees Celsius). Include the following: (1) two accessor methods to return the temperature—one to return the degrees Celsius, the other to return the degrees Fahrenheit—use the following formulas to write the two methods, and round to the nearest tenth of a degree:

DegreesC=5(degreesF−32)/9DegreesF=(9(degreesC)/5+32);

DegreesC=5(degreesF−32)/9DegreesF=(9(degreesC)/5+32);

(2) three mutator methods: one to set the value, one to set the scale (F or C), and one to set both; (3) three comparison methods: an equals method to test whether two temperatures are equal, one method to test whether one temperature is greater than another, and one method to test whether one temperature is less than another (note that a Celsius temperature can be equal to a Fahrenheit temperature as indicated by the above formulas); and (4) a suitable toString method. Then write a driver program (or programs) that tests all the methods. Be sure to use each of the constructors, to include at least one true and one false case for each of the comparison methods, and to test at least the following temperature equalities: 0.0 degrees C = 32.0 degrees F, –40.0 degrees C = –40.0 degrees F, and 100.0 degrees C = 212.0 degrees F.

Write a C++ program to perform various calculations related to the fuel economy of a vehicle where the fuel economy is modeling using a polynomial of the form y = Ax² + Bx + C, where

y = fuel economy in miles per gallon (mpg)

x = speed in miles per hour (mph)

In particular:

Inputs: The user should be prompted to input the following information.

The values for coefficients A, B, and C used to model the fuel efficiency

The capacity of the fuel tank (in gallons).

The current amount of fuel in the tank (in gallons).

The current speed of the vehicle (in mpg)

The distance to be travelled on the current trip (in miles)

The cost per gallon for gasoline

The minimum speed, Smin, to be used in the table of Fuel Economy vs Speed

The maximum speed, Smax, to be used in the table of Fuel Economy vs Speed

The speed increment, Sinc, to be used in the table of Fuel Economy vs Speed

Functions: The program should use at least 4 user-defined functions (in addition to main) as described below.

MPG(A, B, C, Speed) – This function returns the fuel economy in mpg for a given speed in mph.

PrintTable(Smin, Smax, Sinc A, B, C) – This function will print a table of Speed (in mpg) and Fuel Economy (in mpg).

Use the range of speeds indicated with the speed increment indicated.

This function should call the function MPG above.

Fuel economy should be calculated using the coefficients A, B, and C provided.

Include a table heading with units.

Display speeds as integers and fuel economy with 2 digits after the decimal point (include trailing zeros).

MaxEconomy(Smin, Smax, Sinc A, B, C, MaxMPG, MaxMPH) – This function will return the maximum mpg and the corresponding speed value using the speed range and increment specified. This function should call the function MPG above.

Use at least one more useful (user-defined) function to calculate one or more of the program outputs.

Outputs: The program output should include the following:

Neatly summarize the input values

A table of Speed and Fuel Economy values (created by the PrintTable function above).

The maximum fuel economy (in mpg) and the corresponding speed (determined by the MaxEconomy function above).

The fuel economy (in mpg) at the current speed

The minimum fuel economy (in mph) and the corresponding speed. Note: This does not always occur at the minimum speed.

For the current speed, trip distance, number of gallons currently in the tank, and cost per gallon for fuel (show the value of each), display the following:

The fuel economy (in mpg)

Speed for the trip (in mph)

The fuel cost for the trip.

The number of gallons that will be used for the trip.

The time to reach the destination.

State how many times you will need to stop for gas. Assume that the tank must be filled when it is 10% full.

State the number of gallons of gas will be left in the tank at the end of the trip.

State the number of miles until the next time the tank must be filled (after the trip).

Repeat the above if you drive at the speed for maximum fuel economy. Also state how many gallons of gas were saved and how much money was saved by driving at the speed for maximum fuel efficiency.

Use a suitable number of digits for all numeric outputs and include units when appropriate.

Error Checks: The program should check for appropriate ranges for inputs and allow the user to re-enter any incorrect inputs, including:

Fuel tank capacity: 0 to 20 gallons

Current amount of fuel in tank: 20% - 100% of fuel tank capacity

Current speed of vehicle: 20 to 80 mph

Distance to be travelled: Must be > 0

Cost per gasoline: Must be > 0

Minimum speed for table (Smin): Integer value where 20 < Smin < 50

Maximum speed for table (Smax): Integer value where (Smin + 10) < Smax < 80

Speed increment for table (Sinc): Integer value where 0 < Sinc < (Smax – Smin)/5

Re-running the Program: Include a loop that will give the user the option of re-running the program.

Your utility function is U = 10 X 0.1Y 0.7 and your marginal utility functions are MUx=X^−0.9 Y^ 0.7 MUy=7X^ 0.1 Y^−0.3

Your budget is M and the prices of the two goods are pX and pY .

1. a) Write down the two conditions for utility maximization subject to a budget constraint.

2. b) Derive the demand functions for X and Y .

3. c) Based on your demand functions explain whether:

   • - Y is a normal good or an inferior good and why. (1 mark)

   • - good X satisfies the law of demand. (1 mark)

4. d) Assume you currently have 42 units of Y and 3 units of X . How many units of Y are you

   willing to give up for an additional unit of X while holding your total utility constant? (1 mark)

Suppose that the market for gourmet deli sandwiches is perfectly competitive and that the supply of workers in this industry is upward-sloping, so that wages increase as industry output increases. Delis in this market face the following total cost:

TC = q³ - 20 q² + 120 q + W

where,

Q = number of sandwiches

W = daily wages paid to workers

The wage, which depends on total industry output, equals: W = 0.3 Nq

where,

N = number of firms.

Assume that the market demand is:

Q^D = 900 - 10 P

1. What is the long-run equilibrium output for each firm?   

2. How much does the long-run equilibrium price change as the number of firms increases?

3. What is the long-run equilibrium number of firms?  

4. What is the total industry output?   

5. What is the long-run equilibrium price?

Suppose that the market for gourmet deli sandwiches is perfectly competitive and that the supply of workers in this industry is upward-sloping, so that wages increase as industry output increases. Delis in this market face the following total cost:

TC = q³ - 10 q² + 60 q + W

where,

Q = number of sandwiches

W = daily wages paid to workers

The wage, which depends on total industry output, equals: W = 0.3 Nq

where,

N = number of firms.

Assume that the market demand is:

Q^D = 900 - 5 P

1. What is the long-run equilibrium output for each firm?   

2. How much does the long-run equilibrium price change as the number of firms increases?

3. What is the long-run equilibrium number of firms?  

4. What is the total industry output?   

5. What is the long-run equilibrium price?

1. In a company production line, the number of defective parts and their probabilities produced in an hour are shown in TABLE 1. Let x be the number of defective parts in an hour and K is P(X=K):

TABLE 1

1. How many defective parts are expected to be produced in an hour in the company’s production line?                                                                        

2. Compute the standard deviation of the defective parts produced in an hour by the company’s production line.                                              

3. Find the value of P(0 < X £ 3).                                                                         

2. Penny will play 2 games of badminton against Monica. Penny’s chances of winning each game is around 60 %. Let X denotes the number of Penny winning the game.
   1. Construct a probability distribution and cumulative probability distribution table for X.

2. Graph the probability distribution of X.

This problem asks you to do your own growth accounting exercise. Using data since 1960, make a table of annual growth rates of real GDP, the capital stock (private fixed assets from the Fixed Assets section of the BEA website, www.bea.gov, Table 6.2), and civilian employment. Assuming a_K = 0.3 and a_N = 0.7, find the productivity growth rate for each year.

a. Graph the contributions to overall economic growth of capital growth, labor growth, and productivity growth for the period since 1960.   Contrast the behavior of each of these variables in the post–1973 period to their behavior in the earlier period.

b. Compare the post–1973 behavior of productivity growth with the graph of the relative price of energy, shown in Fig. 3.11 of the textbook. To what extent do you think the productivity slowdown can be blamed on higher energy prices?