Hypothesis Testing

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Hypothesis Testing

Activities

STEPS
Tutorials

Interactive computer-based tutorials

Worksheets

'Barramundi' Data

1000 integers with a normal distribution

Distribution of Sample Means

Histograms of distributions for n=1, n=3, n=9

"The great book of nature can be read only by those who know the language in which it is written, and that language is mathematics" - Galileo

Datasets
Visit the Datasets page for more datasets and stories to support this topic.

Or, get some ideas on how students can gather their own data

Websites

Inference, from the Hobart Mercury newspaper.

Chi-square isn't in our syllabuses, but is useful for analysing survey data.

Java Applets

Central Limit Theorem

Introduce the Concept Early!

The concept of hypothesis testing should be introduced informally when first constructing stemplots and histograms. The terminology relating to populations and samples can be introduced early in the study of statistics and used consistently throughout the unit.

For example, after students have constructed a stemplot of Henry Cavendish's data on the density of the earth, the following issues can be discussed:

The data is only a sample of all possible measurements.
Why measurements, even of the same quantity, are not identical.
The true value of the density can be estimated. The idea of a point estimate and an interval estimate arises quite naturally.
The likelihood of the true density being as low as 5.3. A conclusion might be, 'It is highly unlikely that the actual density of the earth is 5.3 or lower.' Students who understand this conclusion are well are their way towards understanding hypothesis testing.

It is worth mentioning at this early stage that there are statistical procedures that allow us to make precise statements about liklihood and that the students will meet these later in the unit.

STEPS

The STEPS modules are a collection of hypertext-based tutorials covering a wide range of statistics topics, including hypothesis testing.. Visit the STEPS page for further information and a list of the modules available.

The 'Barramundi' Dataset

This dataset contains 1000 integers (having a normal distribution with mean=55 and sigma=12. The data fit nicely onto both sides of an A4 sheet of paper. I have used this data to simulate a population of barramundi in the Fitzroy river, but you of course can make up your own scenario.

N.B. The HTML version of the dataset contains 800 integers as that was as many as would fit onto two pages.

Inference in the News

A website containing a collection of articles from the Hobart Mercury newspaper that illustrate various aspects of drawing conclusions from data.

Central Limit Theorem

This applet demonstrates the central limit theorem using simulated dice-rolling experiments.

Hypothesis Testing Joke

This joke is from Mark Eakin (eakin@omega.uta.edu), who has kindly given permission for me to include it on the website.

Most of you do not know that when Santa was a young man he had to take a statistics course. When the class started covering two-sided hypothesis tests, he had a lot of trouble remembering where to put the equal sign. He started repeating to himself "The equal sign goes in the null hypothesis. The equal sign goes in the null hypothesis. The equal sign goes in the null hypothesis."

Eventually Santa had to shorten this phrase to make it easier to remember. In fact to this day you can still hear him say "Ho, Ho, Ho."