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IB DP Maths: AI SL复习笔记4.7.1 Hypothesis Testing

Category: IB课程, 教材笔记, 福利干货 Date: 2022年7月19日下午4:09

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

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 populationA 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 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

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

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