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DP IB Maths: AI SL

Revision Notes

Home / IB / Maths: AI SL / DP / Revision Notes / 4. Statistics & Probability / 4.7 Hypothesis Testing / 4.7.1 Hypothesis Testing


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
    • The null hypothesis is denoted straight H subscript 0 and sets out the assumed population parameter or distribution given that no change has happened
    • The alternative hypothesis is denoted straight H subscript 1 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 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

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 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


  • 1. Number & Algebra
    • 1.1 Number Toolkit
      • 1.1.1 Standard Form
        • 1.1.2 Exponents & Logarithms
          • 1.1.3 Approximation & Estimation
            • 1.1.4 GDC: Solving Equations
            • 1.2 Sequences & Series
              • 1.2.1 Language of Sequences & Series
                • 1.2.2 Arithmetic Sequences & Series
                  • 1.2.3 Geometric Sequences & Series
                    • 1.2.4 Applications of Sequences & Series
                    • 1.3 Financial Applications
                      • 1.3.1 Compound Interest & Depreciation
                        • 1.3.2 Amortisation & Annuities
                      • 2. Functions
                        • 2.1 Linear Functions & Graphs
                          • 2.1.1 Equations of a Straight Line
                          • 2.2 Further Functions & Graphs
                            • 2.2.1 Functions
                              • 2.2.2 Graphing Functions
                                • 2.2.3 Properties of Graphs
                                • 2.3 Modelling with Functions
                                  • 2.3.1 Linear & Piecewise Models
                                    • 2.3.2 Quadratic & Cubic Models
                                      • 2.3.3 Exponential Models
                                        • 2.3.4 Direct & Inverse Variation
                                          • 2.3.5 Sinusoidal Models
                                            • 2.3.6 Strategy for Modelling Functions
                                          • 3. Geometry & Trigonometry
                                            • 3.1 Geometry Toolkit
                                              • 3.1.1 Coordinate Geometry
                                                • 3.1.2 Arcs & Sectors
                                                • 3.2 Geometry of 3D Shapes
                                                  • 3.2.1 3D Coordinate Geometry
                                                    • 3.2.2 Volume & Surface Area
                                                    • 3.3 Trigonometry
                                                      • 3.3.1 Pythagoras & Right-Angled Triganometry
                                                        • 3.3.2 Non Right-Angled Trigonometry
                                                          • 3.3.3 Applications of Trigonometry & Pythagoras
                                                          • 3.4 Voronoi Diagrams
                                                            • 3.4.1 Voronoi Diagrams
                                                              • 3.4.2 Toxic Waste Dump Problem
                                                            • 4. Statistics & Probability
                                                              • 4.1 Statistics Toolkit
                                                                • 4.1.1 Sampling & Data Collection
                                                                  • 4.1.2 Statistical Measures
                                                                    • 4.1.3 Frequency Tables
                                                                      • 4.1.4 Linear Transformations of Data
                                                                        • 4.1.5 Outliers
                                                                          • 4.1.6 Univariate Data
                                                                            • 4.1.7 Interpreting Data
                                                                            • 4.2 Correlation & Regression
                                                                              • 4.2.1 Bivariate data
                                                                                • 4.2.2 Correlation Coefficients
                                                                                  • 4.2.3 Linear Regression
                                                                                  • 4.3 Probability
                                                                                    • 4.3.1 Probability & Types of Events
                                                                                      • 4.3.2 Conditional Probability
                                                                                        • 4.3.3 Sample Space Diagrams
                                                                                        • 4.4 Probability Distributions
                                                                                          • 4.4.1 Discrete Probability Distributions
                                                                                            • 4.4.2 Expected Values
                                                                                            • 4.5 Binomial Distribution
                                                                                              • 4.5.1 The Binomial Distribution
                                                                                                • 4.5.2 Calculating Binomial Probabilities
                                                                                                • 4.6 Normal Distribution
                                                                                                  • 4.6.1 The Normal Distribution
                                                                                                    • 4.6.2 Calculations with Normal Distribution
                                                                                                    • 4.7 Hypothesis Testing
                                                                                                      • 4.7.1 Hypothesis Testing
                                                                                                        • 4.7.2 Chi-squared Test for Independence
                                                                                                          • 4.7.3 Goodness of Fit Test
                                                                                                            • 4.7.4 The t-test
                                                                                                          • 5. Calculus
                                                                                                            • 5.1 Differentiation
                                                                                                              • 5.1.1 Introduction to Differentiation
                                                                                                                • 5.1.2 Applications of Differentiation
                                                                                                                  • 5.1.3 Modelling with Differentiation
                                                                                                                  • 5.2 Integration
                                                                                                                    • 5.2.1 Trapezoid Rule: Numerical Integration
                                                                                                                      • 5.2.2 Introduction to Integration
                                                                                                                        • 5.2.3 Applications of Integration
                                                                                                                      Daniel Finlay

                                                                                                                      Author: Daniel

                                                                                                                      Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.


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