Hypothesis Testing

ECON 309

Lecture 5: Hypothesis Testing

I. Hypotheses

A hypothesis is a claim about a parameter that you’re interested in. The simplest hypotheses are about the parameters of a single variable, such as the mean of a population. But there are more complicated hypotheses, as we’ll see when we get to regression analysis; these hypotheses are about the parameters that control the relationship between two or more variables.

Some simple hypotheses:

• The average number of customers in this store per day is greater than 10.

• Condoms from this production line will break less than 1% of the time.

• The average number of years it takes to graduate from CSUN is 6.5.

To do a hypothesis test, you will actual have two hypotheses: the null hypothesis and the alternative hypothesis, which are stated in such a way that they are mutually exclusive (that is, the hypotheses cannot both be true). The null hypothesis is the conclusion that is considered the default: you will accept (or more accurately, not reject) this hypothesis if you fail to find sufficient support for the alternative hypothesis.

This is important: it means you are placing the burden of proof on those who support the alternative hypothesis. The null hypothesis is essentially “innocent until proven guilty” – it can be accepted with little support from the evidence, simply because the evidence doesn’t strongly indicate something else. For this reason, researchers will usually use the alternative hypothesis to represent their own position – what they wish to prove – in order to put their claim to the strongest test. But sometimes researchers put their own position as the null, in which case they’ve made things very easy on themselves.

II. One-Tail versus Two-Tail Hypo Tests

What if the CSUN administration claims the average number of years to graduate from CSUN is 6.5? There are two ways they could be wrong: the average could be lower, or the average could be higher....