# Midterm Study Guide

The midterm is in class on Friday Oct 27th 2017.

The midterm from last year is provided on canvas.

Material up to and including Wednesday 25th of October could be on the midterm.

## Concepts

Identify the implied and/or justified scope of inference from the description of a study.

Define the key components of a study: population of interest, variable of interest, parameter of interest.

Describe the difference between a population parameter and a sample statistic.

Describe what is meant by the sampling distribution of a statistic.

State the results of key theorems: the Weak Law of Large Numbers, the Central Limit Theorem.

Use the Central Limit Theorem to derive the approximate sampling distribution for a sample mean given population parameters.

For each of the three approaches to figuring out the sampling distribution of a sample statistic (derive, approximate or simulate), give an example of a population distribution and statistic that is amenable to the approach.

In the context of a hypothesis test define type I error rate and power.

Describe the difference between the signifcance level of a test and the Type I error rate of a test.

Describe what it means for an estimate to be unbiased.

Describe what it means for an estimate to be consistent.

Describe what it means for a test to be exact.

Describe what it means for a test to be consistent.

Describe how simulation might be used to evaluate: the bias in an estimate, the consistency of an estimate, the type I error rate of a test, or the power of a test.

Describe the relationship between the power of a Z/t-test and: the population variance, sample size, difference between true mean and hypothesized mean and the significance level.

Use a null distribution (provided via tables or a histogram) to find a rejection region, critical value(s) and or p-value for a test.

Define p-value.

Identify incorrect interpretations of a p-value and/or confidence interval.

## Procedures

You should know how to perform the following test procedures (this includes describing the appropriate setting for the test, the null and alternative hypotheses, the test statistic, the reference distribution, as well as being able to complete the calculations), and be able to write a statistical summary from the results:

• Z-test/confidence interval/p-value
• t-test/confidence interval/p-value
• Exact binomial test/p-value
• Normal approximation binomial test (z-test)/confidence interval/p-value
• Sign test/confidence interval/p-value
• Signed-rank test/p-value
• Chi-squared test for variance/confidence interval/p-value
• Alternative t-test for variance
• Kolmogorov-Smirnov test for distribution