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
5. Salaries of college grads in Chicago and Philadelphia
are thought to be equal.
Find the second derivative with respect to l.
If your memory wasn't so good, then begin with the likelihood
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
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:
b. What is the mean of u?
1. A. Prove that this is a probability density.
Department of Economics
4. The sample drawn from a uniform distribution on [a,
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.
A. Find the average miles per gallon.
2. A gasoline producer sponsors a mileage test.