Assignment Four ECON 2040 Due Date: A01/A02,

Assignment Four ECON 2040

Due Date: A01/A02, December 7, 2015,Monday

A03, December 8, Tuesday

(1) This assignment is to be completed individually. Students are allowed to discuss or share ideas with your fellow student however your answer should be unique and cannot copy others’ work as mentioned in our course outline. Please start working on the assignment right now, drop by at my office if you have any questions. Otherwise you will not have enough time to finish the assignment before due date.

(2) Be sure to create a title page for your assignment, including your name, student number,session number.

(3) Please type the assignment. Please make effort to present your work professionally.

(4) Questions will be chosen from the assignment to mark for your final grade. If you do not do questions that are not chosen to be marked, your marks will be deducted for number of questions that you did not do.

(5) Please hand in the printed out assignment before class. No late assignment will be accepted.

1. What is Type I error for a hypothesis test? What is Type II error for a hypothesis test? How type I error and Type II error is related?

2. What is the power of a test? How do we increase the power of a test?

3. A fitness club claims that the average age of its members is 42. Assume that the ages are normally distributed. You believe that the average age is less than 42, therefore, you ask the ages of a few of the fitness club's members and get the following values: 40, 55, 50, 33, 38, 35, 30, and 45.

· Do you have any reason to think the fitness club's claim is incorrect? Using you knowledge on hypothesis testing, explain your conclusion carefully with detailed procedure.

· Find the p-value of your test, and interpret the results.

· Researchers will state the hypothesis they would like to confirm as alternative hypothesis, why?

4. Use the following example to explain this question, why do you only need to calculate a critical value for a simple hypothesis i.e. μ = c, even if your null is μ ≥ c or μ <= c?

An engineering research center claims that, through the use of a new computer control system, automobiles should achieve, on average, at least an additional 5 miles per gallon of gas. A random sample of 81 automobiles was used to evaluate this product. The sample mean increase in miles per gallon achieved was 4.5, and the sample standard deviation was 2.9 miles per gallon.

State the appropriate null and alternative hypotheses and answer the question.

5. (This is a concept exercise. Please do not hand in your answer ) Based on the computer exercise questions in assignment 3 and 4, could you design a Monte Carlo simulation to show your understanding of confidence interval estimation?