Hypothesis Testing(Ch11, Keller 9th ED.)

There are two hypotheses. One is called the null hypothesis (), and the other the alternative or research hypothesis ( or ).

2. The testing procedure begins with the assumption that the null hypothesis is true.

3. The goal of the process is to determine whether there is enough evidence to infer that the alternative hypothesis is true.

Hypothesis Testing(Ch11, Keller 9th ED.)

4. There are two possible decisions: Conclude that there is enough evidence

to support the alternative hypothesis (Reject H0)

Conclude that there is not enough evidence to support the alternative hypothesis (Do not reject H0)

Conclusions of a Test of Hypothesis (page 374, Keller 9th ED.)

If we reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the alternative hypothesis is true.

If we do not reject the null hypothesis, we conclude that there is not enough statistical evidence to infer that the alternative hypothesis is true.

Ex. H0: Simpson did not kill his wife H1: Simpson killed his wife. It is a bad example in the sense no parameter is

specified, but it helps you understand the concept.

Building Hypothesis

The parameter space is the possible outcome that the parameters can be.

For example, the μ from Normal (μ, ) can range 𝜎from .

We can set up the null by assuming the parameter equal or larger/less than some number in the parameter space.

For example, H0: μ=0 or H0: μ0 or H0: μ0. So that its

corresponding H1 are H0: μ0 or H0: μ0 or H0: μ0. We do two-sided test for the first and one-sided

test for the other two.

Building Hypothesis

But you frequently see someone set up hypothesis and do one-sided test like this:

H0: μ=0 H1: μ<0 H0: μ=0 H1: μ>0 Usually, you do this when you have knowledge

about μ (you know μ has been 0 in this case), but you now have doubt it might change.

Last thing, put equality if necessary to include the case that parameter equals the number you believe or you know (status quo).

Two population mean, proportion, and variance

Now we are interested in comparing the parameters from two populations.

Eg. The difference of means (), the difference of proportions () . They are also called point estimates.

You can test them by finding statistics, then look at appropriate critical value (from t, Z, or F distribution).

About Hw6

Until now, we have covered Difference in means test (−)

Case 1. When pop. var is known, then look at Z Case 2. When pop. var is not known, then use

sampling var, and look at t. Sub-case. If assume two pop. var are equal,

then we can compute the pooled var, and the df. is just -2. (Q1,2,3, HW6)

Sub-case. If assume two pop. var are not equal, then we compute the df. by the formula on page 43. (Q4,5,6, HW7)

About Hw7

Case 3. When samples are dependent, we do the matched pair test. We use t statistics with df equal to . (HW7)

Previous Exam Q

Q24-26 on Page 232, Course Pack In an effort to increase customer service. ….trying

a new data entry program… ╮(－ _－ )╭ Before they do it, they select randomly 7 guys, and

recorded their data entry times with the old and new system.

Step1: Set up hypothesis Step2: find test statistics Step3: find the critical value from correct

distribution. Step4: Make your decision.

Previous Exam Q

Q30-31 on page 234, Course Pack