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Hypothesis Testing (DP IB Maths: AI SL)
Revision Note
Language of Hypothesis Testing
What is a hypothesis test?
- A hypothesis test uses a sample of data in an experiment to test a statement made about the population
- The statement is either about a population parameter or the distribution of the population
- The hypothesis test will look at the probability of observed outcomes happening under set conditions
- The probability found will be compared against a given significance level to determine whether there is evidence to support the statement being made
What are the key terms used in statistical hypothesis testing?
- Every hypothesis test must begin with a clear null hypothesis (what we believe to already be true) and alternative hypothesis (how we believe the data pattern or probability distribution might have changed)
- A hypothesis is an assumption that is made about a particular population parameter or the distribution of the population
- A population parameter is a numerical characteristic which helps define a population
- Such as the mean value of the population
- The null hypothesis is denoted
and sets out the assumed population parameter or distribution given that no change has happened - The alternative hypothesis is denoted
and sets out how we think the population parameter or distribution could have changed
- A one-tailed test is used for testing the distribution or testing whether the parameter has increased (or decreased)
- A two-tailed test is used for testing whether the parameter has changed (either increased or decreased)
- When a hypothesis test is carried out, the null hypothesis is assumed to be true and this assumption will either be accepted or rejected
- When a null hypothesis is accepted or rejected a statistical inference is made
- A population parameter is a numerical characteristic which helps define a population
- A hypothesis test will always be carried out at an appropriate significance level
- The significance level sets the smallest probability that an event could have occurred by chance
- Any probability smaller than the significance level would suggest that the event is unlikely to have happened by chance
- The significance level must be set before the hypothesis test is carried out
- The significance level will usually be 1%, 5% or 10%, however it may vary
- The significance level sets the smallest probability that an event could have occurred by chance
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Conclusions of Hypothesis Testing
How do I decide whether to reject or accept the null hypothesis?
- A sample of the population is taken and the test statistic is calculated using the observations from the sample
- Your GDC will calculate the test statistic for you
- To decide whether or not to reject the null hypothesis you first need either the p-value or the critical region
- The p - value is the probability of a value being at least as extreme as the test statistic, assuming that the null hypothesis is true
- Your GDC will give you the p-value
- If the p-value is less than the significance level then the null hypothesis would be rejected
- The critical region is the range of values of the test statistic which will lead to the null hypothesis being rejected
- If the test statistic falls within the critical region then the null hypothesis would be rejected
- The critical value is the boundary of the critical region
- It is the least extreme value that would lead to the rejection of the null hypothesis
- The critical value is determined by the significance level
- In your exam you will be given the critical value if it is needed
How should a conclusion be written for a hypothesis test?
- Your conclusion must be written in the context of the question
- Use the wording in the question to help you write your conclusion
- If rejecting the null hypothesis your conclusion should state that there is sufficient evidence to suggest that the null hypothesis is unlikely to be true
- If accepting the null hypothesis your conclusion should state that there is not enough evidence to suggest that the null hypothesis is unlikely to be true
- Your conclusion must not be definitive
- There is a chance that the test has led to an incorrect conclusion
- The outcome is dependent on the sample
- a different sample might lead to a different outcome
- The conclusion of a two-tailed test can state if there is evidence of a change
- You should not state whether this change is an increase or decrease
Exam Tip
- Accepting the null hypothesis does not mean that you are saying it is true
- You are simply saying there is not enough evidence to reject it
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