## Statistics

### Hypothesis Tests

A statistical hypothesis test is a method for making decisions using data from an experiment, survey, or an observational study, deciding whether the evidence is sufficient to reject the status quo as described by the null hypothesis. The lessons in this unit focus on developing understanding of central inferential concepts. Students generate random samples, set up hypotheses tests and examine the meaning of p-values and alpha levels, Type I and II errors and their connection to power. They also investigate several different tests and when they are applicable.

### Statistics: Hypothesis Tests Activities

Title Type

#### Meaning of Alpha

• Students will recognize that the alpha value (significance level of a test) is the relative frequency for sample statistic values that lead to a "reject the null" conclusion, given that the null hypothesis is actually true.
• Students will recognize that a sample mean can lead to a "reject the null" or "fail to reject the null" depending on the alpha level.

• 4755

#### Contingency Tables and Chi-Square

This lesson involves deriving and interpreting the chi-square as an indication of whether two variables in a population are independent or associated.

• 3064

#### Chi-Square Tests

This lesson involves investigating chi-squared tests and distributions.

• 3293

#### Difference in Means

This activity involves investigating whether a difference really seems to exist between two sample means.

• 3021

#### Meaning of Power

In this lesson, samples are generated from a population for a particular hypothesis test, leading to the conjecture that the null hypothesis is actually false.

• 4470

#### Type 2 Error

This activity allows students to experiment with different alpha levels and alternative hypotheses to investigate the relationship among types of error and power.

• 3183

#### What is a p-value?

This lesson involves beginning with a null hypothesis specifying the mean of a normally distributed population with a given standard deviation.

• 4255

#### Resampling

This lesson involves approximate sampling distributions obtained from simulations based directly on a single sample. The focus of the lesson is on conducting hypothesis tests in situations for which the conditions of more traditional methods are not met.

• 2919