# Hypothesis Testing

Hypothesis testing is a fundamental concept in statistics used to make inferences about a population based on a sample of data. It involves formulating two competing hypotheses (the null hypothesis and the alternative hypothesis) about a parameter of interest and then using sample data to determine which hypothesis is more likely or supported by the evidence.

The two main hypotheses involved in hypothesis testing are:

Null Hypothesis (Hₒ): The null hypothesis represents the default assumption or the statement of no effect, no difference, or no relationship. It is often denoted by Hₒ and is typically the hypothesis that researchers want to test or challenge.

Alternative Hypothesis (H₁): The alternative hypothesis represents the opposite of the null hypothesis and expresses what the researcher hopes to demonstrate or prove. It is denoted by H₁ and describes the or relationship the researcher is investigating.

Hypothesis testing is a powerful tool for making data-driven decisions and drawing inferences about populations. It is widely used in various fields such as medicine, social sciences, business, and engineering to test theories, validate claims, and support evidence-based decision-making.

For the H2 A Level exams, only hypothesis for mean is tested. (Note: for those of you taking ACT, SAT 2, or AP, you’ll also need to know the hypothesis testing for proportion.)

## Hypothesis Testing Using p-test method or test statistic method

We often use the p-test method or the test statistic method for hypothesis testing for H2 A Level Math exam.

## Hypothesis Testing: p-test method

Doing a hypothesis testing via the p-test method involves these steps:

1. Define the null hypothesis and the alternative hypothesis
2. State whether it is a one-tail or two-tail test
3. State the level of significance in the hypothesis test
4. If the distribution is not a normal distribution, assume that it is by Central Limit Theorem (if n is large e.g. n> 20).
5. Find the p-value
6. Compare the p-value with the level of significance to determine whether you reject or accept Hₒ. We only reject Hₒ when p value is less than the level of significance.

### Using the graphic calculator for p-test method:

• Press [Stat] button, then go to Test, and select Z-test
• Press in the information you have and you’ll get p- value.
• Compare p- value with level of significance to determine whether you reject or accept Ho.

## Hypothesis Testing: Test Statistics Method

Doing a hypothesis testing via the test statistics method involves these steps:

1. Define the null hypothesis and the alternative hypothesis
2. State whether it is a one-tail or two-tail test
3. State the level of significance in the hypothesis test, and determine the critical region
4. If the distribution is not a normal distribution, assume that it is by Central Limit Theorem (if n is large e.g. n> 20).
5. Find the test statistics using the formula:

6. Compare the test statistics with the critical region to determine whether you reject or accept Hₒ. We only reject Hₒ when when test statistics lies within the critical region.

## How to approach H2 A Level Math Statistics Questions

Want a complete course on hypothesis testing and the whole of H2 A Level Math Statistics?

Check out our course here, where we cover all the topics tested in statistics.

The course includes concepts, types of questions, and how to apply them, so that you’ll score for your exam.

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