6. The Poisson and a Wald test: You are given the data:

Since the observed t lies outside the acceptance region, we reject the null of equal salaries.

The test statistic will be

We will suppose that the variance is the same for both groups. In which case a pooled estimate of the common variance is

5. Salaries of college grads in Chicago and Philadelphia are thought to be equal.

Find the second derivative with respect to l.

Expand the result

Take logs:

If your memory wasn't so good, then begin with the likelihood function:

The critical value is larger thanb the observed chi-square, so do not reject the null.

If you have a good memory then you could just plug into the memorized formula. I have done it using the sample mean and sample variance as estimates of the population variance.

Compute the sample mean and variance. For a Poisson r.v. we would expect the sample mean and variance to be nearly equal.

Exploiting a little subtlety:

Using brute force:

C. What is the variance?

b. What is the mean of u?

1. A. Prove that this is a probability density.

Temple University

Department of Economics

Econometrics I

Econ 615

Mid-term Exam

Answer Key

C. Method of moments

B. The sample variance

A. The sample mean

4. The sample drawn from a uniform distribution on [a, b] is

C. The test for independence is whether the product of the marginals is equal to the intersection. P(A and B) = P(A)P(B) ?

Since P(A and B) = 1/6 and P(A) = 1/2 and P(B) = 1/3 we can see that the equality holds and therefore the events are independent.

B. The probability of an even number is 1/2. The probability of a number less than 3 is 1/3. We already know the probability of the intersection is 1/6. Therefore P(A or B) = 3/6+2/6-1/6 = 2/3.

A. There are six faces on a die. There is only one way that youcan roll an even number and a number that is less than 3. Therefore, P(A and B) = 1/6.

3. Roll a fair die.

B. Find the variance

A. Find the average miles per gallon.

2. A gasoline producer sponsors a mileage test.