Temple Uinversity
Department of Economics
Econ 8009

Probability, Statistics and Hypothesis Testing
1 Peanuts

Solve for m and s.

What is the probability of more than 7 ouces per jar?

2 Mean and variance of two estimators
a. True
b. True
c. 1/3 s2.
d. 7/18 s2.

3. Daily output

Critical t with 24 deg of freedom and .005 in the tail = -2.79

There is no difference.
4.  Two magazines

The observed t falls in the do not reject region.  Sales are the same on the two campuses. 
5. Fair dice?

Using the normal approximation we see a huge Z score.

The Wald statistic is given by the following for the relative frequency or the count

6. Porpoise counting
a, b. and c. Rate of sighting:  Mammals seen / hours watching.

d.  LM test statistic 
Poisson density

The LM test for a one parameter density is the slope of the likelihood divided by minimum variance given from the information matrix evluated at the restriction. 
The log likelihood for the observed sample is

7 A likelihhood ratio test
The density is

So the likelihood is

As an example for the value to be taken by the LM.  

A graph shows us what it looks like.