CORRELATION AND SIMPLE REGRESSION

QSO 510 Quantitative Analysis for Decision Making

Summer 2012 Mid-term Exam - Instructor: Dr. Derek Kane

Instructions

1. This exam is taken in-class, you may use any notes or books that you care to. You may only use your own notes.

2. The exam only requires the use of a hand calculator. You may use notes you have taken on the

3. Answer all questions in the context of the problem. General answers are not expected.

4. You must show all steps including formulas used and all calculations done to arrive at the final answers. Incomplete solutions will receive partial credit.

5. Use at least four significant digits at all intermediate steps. Round off the final answers appropriately. Note: 0.0042 is only two significant digits as leading zeros are not considered significant. Trailing zeros are considered significant.

6. You only need to do four problems. If you do all five problems indicate which four you want me to grade.

7. You are welcome to ask questions you have on the problems. Please do not ask any questions relating to the solution of any problem.

8. You must work on the exam by yourself.

(For Instructor’s use)

Problem 1 (25 points)

You have an assembly line which produces 50kg bags of flour with a standard deviation of 2.0kg.

a) Assuming the distribution of weight is normal, what is the chance any single bag’s weight is less than 49kg?

b) If you chose 81 bags at random, what would be the expected average weight of the bags in your sample? What would the standard deviation of the sample average be? What is the shape of this distribution? Give reasons for your answers .

c) If you pulled a sample of 64 bags, what is the chance that you would find the average weight was between 49.25 and 50.25kg?

Write your answers in the space below and continue on the next page.

a) The probability we are looking for is

Thus there is a 30.85% chance that the weight will be less than 49kg.

b) Because there are more than 30 items in the sample, the Central Limit Theorem applies and

The shape is Gaussian.

c) The probability is:

There is an 84% chance that the sample will weigh between 49.25 and 50.25.

Problem 2 (25 points)

We want to look at economic opportunity for women. Gallup conducted a survey of women’s employment in Greece and found that 205 of 500 women surveyed were employed

a) Compute the proportion and standard deviation of Greek women who are employed.

b) Construct a 95% confidence interval for women’s employment in Greece.

c) If you are working for CNN, how would you explain the confidence interval to your audience? Does the confidence interval seem small enough? If not, how would you make the interval smaller? Provide a clear and complete answer.

Begin your answer below and continue on the next page.

a) The proportion and standard deviation is

b) The confidence interval is

c) This is the range where we are 95% sure the true proportion lies. We should take a larger sample to get a smaller confidence interval.

Problem 3 (25 points)

According to the same Gallup poll, 46% of men in Greece are employed. Perform a 95% hypothesis test to determine whether the survey of 500 women showing 41% employment indicates that women have a lower employment rate than men in Greece.

Begin your answer below and continue on the next page.

The hypotheses are

The value of α is given as 0.05 and the number of people in the survey is n=500

The threshold of this one-sided z-test is 1.645

The proportion is so the z-statistic is

We accept the alternate hypothesis.

There is statistical evidence that women in Greece have a lower employment rate than men.

Problem 4 (25 points)

The following table shows the Housing Starts in thousands for the past five quarters.

(a)