STA220 Module 10- Hypothesis Testing about a Population Proportion

What is a statistical hypothesis test?

1. See a pattern

2. Acknowledge that the pattern might be explainable or might simply occur by chance

3. Determine any possible explanations are so unlikely they probably didn’t happen

4. Conclude that the observed pattern didn’t arise by chance

WHat is a hypothesis defined as?

The statement about a population; a prediction about a parameter describing some characteristics of a variable (ex: true mean, p) takes a particular numerical value or falls in a certain range of values

How do you conduct a significance test?

Researches (you) use the data to summarize the evidence about a hypothesis

• you can compare the point estimates of a parameters to the values predicted by the hypothesis

What are two important ideas about hypothesis testin?

They all boil down to the same question: is an observed difference or pattern too large to attribute to chance alone?

• measure “how large” by putting our sample results in context of a sampling distribution model (ex: normal model, t distribution)

How do you plan a statistical hypothesis, specifying the model?

You have to specify the model you will use to test the null hypothesis and the parameter of interest

• all model require assumptions so you will need to state them and check any corresponding conditions

• if conditions are satisfied, we can model the sampling distribution of the sample mean with a normal model

• otherwise we cannot proceed with the test (we need to stop and reconsider)

What are the steps in conducting hypothesis testing?

1. State the null and the alternative hypothesis

2. check the necessary assumptions

3. identify the test-statistic (find the value of it)

4. find the p-value of the test-statistic

5. state (if any conclusion)

Step 1 of conducting hypothesis testing

Set up the null and alternative hypothesis: