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IB Mathematics AI HL

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• 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)
• 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)
• A two-tailed test is used for testing whether the parameter has changed (either increased or decreased)
• When a null hypothesis is accepted or rejected a statistical inference is made
• 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.

• 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
• 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
• If the test statistic falls within the critical region then the null hypothesis would be rejected
• It is the least extreme value that would lead to the rejection of the null hypothesis
• 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
• 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
• There is a chance that the test has led to an incorrect conclusion
• a different sample might lead to a different outcome
• You should not state whether this change is an increase or decrease
• You are simply saying there is not enough evidence to reject it

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applications and  interpretation

The main documents (tests and solutions) are in pdf form.

Notice for teachers: word  files are also provided; feel free to use any parts of the tests.  

• [Test 1]       [solutions]       [word]         Lines, Quadratics, Functions, Sequences  (2020)
• [Test 2]     [solutions]       [word]          Functions, Transformations, Logarithms, Financial (2020)
• [Test 3]     [solutions]       [word]           Descriptive Statistics and Probability (2021)
• [Test 4]     [solutions]      [word]           Derivatives (2021)
• [Test 5]     [solutions]       [word]           Integrals (2021)

CUMULATIVE TESTS - MOCK EXAMS

• [Exam 1]    [solutions]    [word]           Sequences, Exponents and Logarithms, Functions, Modelling
• [Exam 2]   [solutions]     [word]           Trigonometry, Descriptive Statistics, Probability distributions

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Hypothesis Testing ( DP IB Maths: AI SL )

Revision note.

Language of Hypothesis Testing

What is a hypothesis test.

• 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)
• 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)
• A two-tailed test is used for testing whether the parameter has changed (either increased or decreased)
• When a null hypothesis is accepted or rejected a statistical inference is made
• 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.

• 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
• 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
• If the test statistic falls within the critical region then the null hypothesis would be rejected
• It is the least extreme value that would lead to the rejection of the null hypothesis
• 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
• 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
• There is a chance that the test has led to an incorrect conclusion
• a different sample might lead to a different outcome
• You should not state whether this change is an increase or decrease
• You are simply saying there is not enough evidence to reject it

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Author: Dan

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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i see a lot of math aa people here if there is anyone from ai esp hl please help. I'm going to fail my math exams for sure seeing as to how I'm doing in the subject so please if y'all have any resources related please share anything literally anything would be of great help 🙏🙏.

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IB Mathematics AI SL - Questionbank

Hypothesis testing.

Hypotheses (Ho/H1), Significance Levels, P-Values, x^2 Tests for Independence & Fit, T-Tests, 1 & 2 Tailed Tests...

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Frequently Asked Questions

What is the IB Math AI SL Questionbank?

The IB Math Applications and Interpretation (AI) SL Questionbank is a comprehensive set of IB Mathematics exam style questions, categorised into syllabus topic and concept, and sorted by difficulty of question. The bank of exam style questions are accompanied by high quality step-by-step markschemes and video tutorials, taught by experienced IB Mathematics teachers. The IB Mathematics AI SL Question bank is the perfect exam revision resource for IB students looking to practice IB Math exam style questions in a particular topic or concept in their AI Standard Level course.

Where should I start in the AI SL Questionbank?

The AI SL Questionbank is designed to help IB students practice AI SL exam style questions in a specific topic or concept. Therefore, a good place to start is by identifying a concept that you would like to practice and improve in and go to that area of the AI SL Question bank. For example, if you want to practice AI SL exam style questions involving Compound Interest & Depreciation, you can go to AI SL Topic 1 (Number & Algebra) and go to the Financial Mathematics area of the question bank. On this page there is a carefully designed set of IB Math AI SL exam style questions, progressing in order of difficulty from easiest to hardest. If you’re just getting started with your revision, you could start at the top of the page with Question 1, or if you already have some confidence, you could start at the medium difficulty questions and progress down.

How should I use the AI SL Questionbank?

The AI SL Questionbank is perfect for revising a particular topic or concept, in-depth. For example, if you wanted to improve your knowledge of Sequences & Series, there is a designed set of full length IB Math AI SL exam style questions focused specifically on this concept. Alternatively, Revision Village also has an extensive library of AI SL Practice Exams, where students can simulate the length and difficulty of an IB exam with the Mock Exam sets, as well as AI SL Key Concepts, where students can learn and revise the underlying theory, if missed or misunderstood in class.

What if I finish the AI SL Questionbank?

With an extensive and growing library of full length IB Math Applications and Interpretation (AI) SL exam style questions in the AI SL Question bank, finishing all of the questions would be a fantastic effort, and you will be in a great position for your final exams. If you were able to complete all the questions in the AI SL Question bank, then a popular option would be to go to the AI SL Practice Exams section on Revision Village and test yourself with the Mock Exam Papers, to simulate the length and difficulty of an actual IB Mathematics AI SL exam.