CORRELATION AND SIMPLE REGRESSION

QSO 510 Quantitative Analysis for Decision Making

Winter 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 5kg bags of flour with a standard deviation of 0.5kg.

a) Assuming the distribution of weight is normal, what is the chance any single bag’s weight is between 4.8kg and 5.2kg?

b) If you chose 60 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 less than 4.95kg?

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

a) We have

Calculate the z-scores

Look up the probabilities and finish.

b) The mean is still 5, the standard deviation is

The shape is Gaussian because we have more than 30 items in the sample and the Central Limit Theorem applies.

c) We have

Calculate the z-scores

Look up the probabilities and finish.

Problem 2 (25 points)

We want to look at US attitudes toward the federal government. Suppose that we sample 1011 US citizens about whether they are satisfied with the size and power of the federal government and find that 293 are satisfied with the size and power of the federal government.

a) Compute the sample proportion and sample standard deviation of people who are satisfied with the federal government’s size and power.

b) Construct a 95% confidence interval for people who support President Obama’s decision.

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 sample proportion is:

0.2898

The standard deviation is

b) The 95% confidence interval is

c) We are 95% sure that the true portion of the population satisfied with the federal government’s size and power is in this range. Make the interval smaller by using a larger sample.

Problem 3 (25 points)

According to a recent Gallup Poll 63% of all US adults are dissatisfied with the size and influence of major corporations. You perform a survey of 100 US citizens who identify themselves as political independents and find that 71 are dissatisfied with the size and influence of major corporations. Perform a hypothesis test to determine whether your survey indicates that political independents have a different view of corporate influence than the general US population.

Begin your answer below and continue on the next page.

Step 1:

H0:

Ha:

Step 2:

z-test because it is a population proportion problem.

Step 3:

Step 4:

Threshold is (95% confidence, two-sided test):

Accept Ha if z-score < -1.96

Accept H0 if -1.96 ≤ z-score ≤ 1.96

Accept Ha if z-score > 1.96

Step 5:

Step 6:

Calculate the z-score

Accept the null hypothesis, H0.

Step 7:

We don’t have statistical evidence indicating that political indenpendents differ from the rest of the population.

Problem 4 (25 points)

The following table shows the life expectancy for 5 countries and the logarithm to the base 10 (log10) of income in these same countries.

(a)