IB DP Maths: AI SL复习笔记4.7.1 Hypothesis Testing
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
A?one-tailed test?is used for testing the distribution or testing whether the parameter has increased (or decreased)
- Such as the mean value of the population
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- 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
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?thenthe?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 the null hypothesis is unlikely true
- If?accepting the null?hypothesis your conclusion should state that there is?not enough evidence?to suggest null hypothesis is unlikely 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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