Ch. 8: The logic of hypothesis testing:

State a hypothesis about a population.

Obtain a random sample from the population.

See if the sample data are consistent with the hypothesis.

The step-by-step procedure:

0. Research question

1. State the hypotheses (null & alternative) & select (alpha).

2. Locate the critical region (s).

3. Collect data and compute test statistic.

4. Make a decision about the null hypothesis and

5. Answer the research question in English.

Let's walk through this for a z-test (in which our test statistic is a z-score).

0. Research question

How does the height of UO men compare to the eight of 19^th century Englishmen?

1. State the hypotheses (null & alternative) & select (alpha).

H₀: µ_{uo Men =} µ_{19thC Men} OR

Words: Null hypothesis: UO men and 19^th C Englishmen are, on average, the same height.

H_A: µ_{uo Men ____} µ_{19thC Men}

Alternative hypothesis (H_A or H₁): UO men are ____________ 19^th C Englishmen

* Need to decide whether to use directional or non-directional hypothesis.

......& select (alpha)

Alpha = probability of a type I error (false +)

We'll use: __________

2. Locate the critical region (s).

3. Collect data and compute test statistic.

Our test statistic is Z: the Z score for x-bar.

Z = x-bar-µ / SE

SE = sigma / n

Note: We happen to know what µ & sigma are for 19^th C Englishmen: very convenient.

4. Make a decision about the null hypothesis

_______________________________________

5. Answer the research question in English.

______________________________________

Question: Why do focus on the null hypothesis when what we are really interested in is the alternative (research) hypothesis?

Answer: The null hypothesis (which states that the myuu we don't know is the same as the myuu we do know) allows us to use the known myuu to "anchor" our sampling distribution. Then we see if the x-bar we got actually fits this assumption. If it doesn't (because it is too extreme to be a typical x-bar for the known myuu) we concluded that the two populations have different myuus.