IV. Statistical Inference

You must be able to decide which statistical inference procedure is appropriate in a given setting. Working lots of review problems will help you.

You need to know the difference between a population parameter, a sample statistic, and the sampling distribution of a statistic.

On any hypothesis testing problem:

1.State hypotheses in words and symbols.

2.Identify the correct inference procedure and verify conditions for using it.

3.Calculate the test statistic and the P-value (or rejection region).

4.Draw a conclusion in context that is directly linked to your P-value or rejection region.

On any confidence interval problem:

1.Identify the population of interest and the parameter you want to draw conclusions about.

2.Choose the appropriate inference procedure and verify conditions for its use.

3.Carry out the inference procedure.

4.Interpret your results in the context of the problem.

You need to know the specific conditions required for the validity of each statistical inference procedure -- confidence intervals and significance tests.

Be familiar with the concepts of Type I error, Type II error, and Power of a test.

Type I error: Rejecting a null hypothesis when it is true.  P(Type I error) = alpha.

Type II error: Accepting a null hypothesis when it is false.

Power of a test: Probability of correctly rejecting a null hypothesis

Power = 1 - P(Type II error).

You can increase the power of a test by increasing the sample size or increasing the significance level (the probability of a Type I error).