Hypothesis Testing is very important in Statistics. There are many different types of hypothesis testing. The hypothesis test used is determined by the information that you are given. Several types of hypothesis tests will be demonstrated in this section. The most common tests are for population means or proportions.
The videos in this section will discuss general properties of hypothesis tests. Topics include ways to reach a decision, types of errors in hypothesis testing, and general characteristics. This area will expand over time.
Definition of Hypothesis Test and General Steps
Setting up the Null and Alternative Hypotheses
Types of Errors in Hypothesis Tests
Interpreting Type I and Type II Errors
Using P-values to Make a Decision
Using Rejection Region to Make a Decision
Determine the Tail of a Hypothesis Test
How to Interpret a Decision in Hypothesis Testing
z-Test for the Mean
A z-test is used when testing a hypothesis about the population mean, and the population standard deviation is known. Majority of the time the population standard deviation will not be known, so this is the less likely of the two tests for a single mean to be used. All tests will be performed by hand and also with the assistance of the TI-84 family and TI-nspire graphing calculators. Both the p-value and rejection region decision rules will be used.
A t-test is used when testing a hypothesis about the population mean, and only the sample standard deviation is known. Majority of the time the population standard deviation will not be known, so this is the more likely of the two tests for a single mean to be used. All tests will be performed by hand and also with the assistance of the TI-84 family and TI-nspire graphing calculators. Both the p-value and rejection region decision rules will be used.
A 1-proportion z-test is used when testing a hypothesis about a population proportion. The 1-proportion z-test will be performed by hand and also with the assistance of the TI-84 family and TI-nspire graphing calculators. Both the p-value and rejection region decision rules will be used.
1-Proportion Z-Test Using a Rejection Region
1-Proportion Z-Test Using a P-value - TI-84
1-Proportion Z-Test Using a P-value - TI-Nspire
1-Proportion Z-Test Draw Normal Curve - TI-Nspire
1-Proportion Z-Test Given Percent TI-84
1-Proportion Z-Test Given Percent TI-Nspire
1-Proportion Z-Test Given Percent Rejection Region
2 Sample Z-test
A 2 Sample Z-test is used when testing a hypothesis about two independent sample means and the population standard deviation is known. I demonstrate how to do this using hand calculations, TI-84, and TI-Nspire. The 2-Sample Z-Test is no used as often as the 2-Sample T-Test, because typically we do not know the population standard deviation.
2-Sample Z-test Using TI-84
2-Sample Z-test Using TI-Nspire
2-Sample Z-test Using Rejection Region
2 Sample T-test
A 2 Sample T-test is used when testing a hypothesis about two independent sample means. I demonstrate how to do this using hand calculations, TI-84, and TI-Nspire. There are two options as to whether to pool or not pool the variances. The variances should only be pulled to calculate the standard error when the population variances for the two samples are the same. There is also a 2-sample t-test for dependent samples that will be discussed at a later time.
Find Critical Value for a 2-Sample T-test
2-Sample T-test Using Rejection Region (independent samples, not pooled)
2-Sample T-test TI-84 (independent samples, not pooled)
2-Sample T-test TI-Nspire (independent samples, not pooled)
2-Sample T-test Rejection Region (independent samples, pooled)
A 2 Proportion Z-test is used when testing a hypothesis about two independent sample proportions. I demonstrate how to do this using hand calculations, TI-84, and TI-Nspire. In order to run this test, the samples need to be independent and randomly selected. You also need to demonstrate that the sample sizes are large enough in order for the central limit theorem to kick in.