A Level Maths

A Level Maths

Maths A-Level Resources for AQA, OCR and Edexcel

A-Level Maths Statistical Hypothesis Testing

Everything you need to know about statistical hypothesis testing for A-Level Maths. Save countless hours of time!

Statistical Hypothesis Testing Topics for A-Level Maths

This module will teach you the following:

Hypothesis testing in a binomial distribution

Hypothesis testing in a normal distribution, hypothesis test using pearson’s correlation coefficient, what’s included.

We’ve created 52 modules covering every Maths topic needed for A level, and each module contains:

  • An editable PowerPoint lesson presentation
  • Editable revision handouts
  • A glossary which covers the key terminologies of the module
  • Topical mind maps for visualising the key concepts
  • Printable flashcards to help students engage active recall and confidence-based repetition
  • A quiz with accompanying answer key to test knowledge and understanding of the module

As a premium member, once rolled out you get access to the entire library of A-Level Maths resources. For now, we have made the first five topics completely free of charge for you to get a taste of what’s to come.

A Level Maths Resources Mapped by Exam Board

Once completed our modules can be used with both UK and international A Level examination board specifications.

We will put together comprehensive mapping documents which will show you exactly which modules align to the specification you are teaching or learning.

hypothesis testing with normal distribution a level maths

Statistical Hypothesis Testing Topics:

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Up Learn – A Level maths (edexcel) – Testing a Population Mean

Hypothesis testing: normal distribution.

Here’s a summary of everything you need to know about hypothesis testing for normal distributions at A Level.

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More videos on Testing a Population Mean:

Introduction to Testing a Population Mean (free trial)

Sample Means and Population Means (free trial)

How Sample Size Affects Sample Means (free trial)

Probabilities of Sample Means (free trial)

Modelling the Sample Mean (free trial)

The Standard Deviation of the Sample Mean’s Distribution (free trial)

When Should We Question Our Population Mean? (free trial)

Finding Critical Regions and Critical Values (free trial)

What Are the Hypotheses? (free trial)

Performing a One-Tailed Test for a Population Mean (free trial)

Performing a Two-Tailed Test for a Population Mean (free trial)

Testing a Population Mean with the Standard Normal Distribution (free trial)

Hypothesis Tests

Hypothesis testing, testing a population mean, testing a pmcc.

Here’s a reminder of the key points you should know about testing a population mean.

Population means and sample means are often different. 

But the bigger the sample, the closer the sample mean is likely to be to the population mean.

If a population is modelled using a normal distribution…

It’s possible to model the probabilities of observing different sample means like this.

Where ‘X bar’ represents the sample mean and n is the sample size.

Then, the variance of the new distribution is this  and the standard deviation is this.

If we have an estimate for a population mean, we can test it out using hypothesis testing.

The logic goes: if the estimate is correct, we’re very unlikely to observe some sample means. 

So if we take a sample and do observe those unlikely means, we should reject the estimate we currently have.  

To find critical regions on a normal distribution, use the inverse normal distribution function on your calculator. 

The hypotheses look pretty much the same as when we test using a binomial distribution.

It’s just that, since we’re forming hypotheses about mean values now, we use.

Finally then, the exam may tell you a sample was taken, tell you the significance level and ask you to perform the rest of the hypothesis test. 

Here’s what that looks like for a one-tailed test.

First, write down the null and alternative hypotheses.

Second, write down the distribution for the sample mean.

Third, find and state the critical region.

Fourth, compare the test statistic to the critical region.

And fifth, write a conclusion.

An alternative method is to find the probability of observing the sample mean or anything greater,

Compare that to the significance level, and then write the conclusion accordingly.

The working looks very similar for a two-tailed test.

Third, find and state the critical region, now with two tails.

And fifth, write a conclusion. 

In place of this step, you could find the probability of observing the sample mean or anything greater,

Compare that to half of the significance level, since this is a two-tailed test, 

And then write the conclusion accordingly.

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Written by real examiners exclusively for Up Learn in order to give you additional confidence when preparing for exams

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Bespoke assessment and practice questions to chart your grade gains as you progress through your A Level Maths revision

hypothesis testing with normal distribution a level maths

Stats 2 Ch3 - Normal Distribution

Home GCSE A-Level Exam Papers

Video Tutorial - Normal Distribution Introduction

Video Tutorial - Normal Distribution to Find Probabilities

Video Tutorial - Inverse Normal Distribution Function

Video Tutorial - Standard Normal Distribution to Find Mean and Standard Deviation

Exam Questions

Mark Scheme

IMAGES

  1. Hypothesis Test on Sample Mean of Normal Distribution

    hypothesis testing with normal distribution a level maths

  2. Hypothesis Testing with the Normal Distribution

    hypothesis testing with normal distribution a level maths

  3. Normal Distribution: Hypothesis Testing (Critical Region)

    hypothesis testing with normal distribution a level maths

  4. Hypothesis testing for Normal Distribution

    hypothesis testing with normal distribution a level maths

  5. 15 Hypothesis Testing with Normal Distributions Chapter 3 Section 7 part 2 Edexcel Applied A Level

    hypothesis testing with normal distribution a level maths

  6. S2

    hypothesis testing with normal distribution a level maths

VIDEO

  1. MATH 1342

  2. Normal Distribution practicals & Hypothesis testing

  3. S2: Hypothesis Testing Normal Distribution Part 1

  4. Binomial Distribution & Hypothesis Testing

  5. Hypothesis Testing with Normal Distribution

  6. CCEA Hypothesis testing question from their Topic Questions

COMMENTS

  1. 5.3.2 Normal Hypothesis Testing

    How is the critical value found in a hypothesis test for the mean of a normal distribution? The critical value(s) will be the boundary of the critical region. The probability of the observed value being within the critical region, given a true null hypothesis will be the same as the significance level; For an % significance level: . In a one-tailed test the critical region will consist of % in ...

  2. Normal Distribution Hypothesis Tests

    Normal Distribution Hypothesis Tests Example Questions. Question 1: Perform a two tail hypothesis test on X\sim N (300,25) with significance level 1\%, having observed 288. Question 2: The journey times by car to Brighton from London had an average of 63 minutes in 2019, with a standard deviation of 2 minutes.

  3. Hypothesis testing for Normal (A-level Maths)

    Answers: Your turn. Let μ be the mean time taken by all Parkrun participants. H 0: μ = 30.3 H 1: μ ≠ 30.3 Significance level α =0.05 This is a 2-tailed test so we use α/2 = 0.025. The distribution of sample means under H 0 is ~ N (30.3, ) so we use for the standard deviation.. Observed sample mean = 30.9 In this case > μ so we're working at the upper end of the distribution.

  4. Edexcel A Level Maths: 3.7 Hypothesis Testing with the Normal ...

    https://www.buymeacoffee.com/zeeshanzamurredPearson A level maths, applied year 2 textbook (3.7) In this video I cover: 1. Hypothesis testing with the normal...

  5. Maths Genie

    AS Level Mechanics and Statistics - Hypothesis Testing. Maths revision videos and notes on the topics of hypothesis testing, correlation hypothesis testing, mean of normal distribution hypothesis testing and non linear regression.

  6. Hypothesis Testing

    A hypothesis test is the means by which we generate a test statistic that directs us to either reject or not reject the null hypothesis. The test statistic is a "summary" of the collected data, and should have a sampling distribution specified by the null hypothesis. A Level AQA Edexcel OCR.

  7. Hypothesis Testing

    This page looks at Hypothesis testing. Topics include null hypothesis, alternative hypothesis, testing and critical regions. The parameters of a distribution are those quantities that you need to specify when describing the distribution.For example, a normal distribution has parameters μ and σ 2 and a Poisson distribution has parameter λ.. If we know that some data comes from a certain ...

  8. PDF S2 Hypothesis tests

    Use a 5% level of significance and state your hypotheses clearly. 2. A report states that employees spend, on average, 80 minutes every working day on personal use of the Internet. A company takes a random sample of 100 employees and finds their mean personal Internet use is 83 minutes with a standard deviation of 15 minutes.

  9. Statistical Hypothesis Testing

    Statistical Hypothesis Testing Topics for A-Level Maths. This module will teach you the following: Hypothesis testing in a binomial distribution. Hypothesis testing in a normal distribution. Hypothesis test using Pearson's correlation coefficient. Download the Sample Chapters →.

  10. Hypothesis Testing: Normal Distribution

    To find critical regions on a normal distribution, use the inverse normal distribution function on your calculator. The hypotheses look pretty much the same as when we test using a binomial distribution. It's just that, since we're forming hypotheses about mean values now, we use.

  11. Normal Distribution (inc. Hypothesis Tests)

    Session Recordings. Normal and Inverse Normal Distribution. Finding the Mean and SD of a Normal Distribution. Normal Hypothesis Tests for Sample Mean. Critical Region for a Normal Hypothesis Test. Normal Approximation to Binomial Distribution.

  12. PDF Hypothesis Testing for Normal Mean

    The biologists use the results of the survey to test, at the 5% level, the hypothesis H 0: μ = 26.1 against the hypothesis H 1: μ ≠ 26.1. (c) Assuming that the distribution of the masses of adult male voles may be modelled by the Normal distribution with the value for the variance found in part (b), calculate the critical region for this ...

  13. PDF Stats 2 Hypothesis Testing Questions

    2-tailed test crit under Ho Allow use Of t method AWFW 0.99 to 1.00 (allow 1) Or z = 1.96 On their z and critical value Or t Accept Ho at 5% level Of significance. Sufficient evidence at the 5% level Of significance to support the manufacturer's belief. Total 6(a) 471 = 94.2 - 6.058 4 1 -tailed test --2.132 Ho Hi : p < 100 94.2-100 --2.14 6.058

  14. MrModoniMaths.com

    A-Level. Pure 1 Ch1 - Algebraic Expressions. Pure 1 Ch2 - Discriminant. ... Regression Correlation and Hypothesis Testing. Stats 2 Ch2 - Conditional Probability. Stats 2 Ch3 - Normal Distribution. Exam Papers ... Standard Normal Distribution to Find Mean and Standard Deviation. Exam Questions. Mark Scheme Page updated ...

  15. Hypothesis Testing (Normal Distribution)

    CIE A Level Maths: Statistics 2 exam revision with questions, model answers & video solutions for Hypothesis Testing. ... Hypothesis Testing 3.3 Hypothesis Testing (Normal Distribution) 3.3 Hypothesis Testing (Normal Distribution) Download. Download View; Easy: Download Questions: View Answers: Medium: ... She uses the data to carry out a ...

  16. 4.3.3 Standard Normal Distribution

    Revision notes on 4.3.3 Standard Normal Distribution for the AQA A Level Maths: Statistics syllabus, written by the Maths experts at Save My Exams. ... 5.3 Hypothesis Testing (Normal Distribution) (A Level only) 5.3.1 Sample Mean Distribution; 5.3.2 Normal Hypothesis Testing; 6. Large Data Set. 6.1 Large Data Set.

  17. 5.2.1 Binomial Hypothesis Testing

    How is a hypothesis test carried out with the binomial distribution? The population parameter being tested will be the probability, p in a binomial distribution B(n , p); A hypothesis test is used when the assumed probability is questioned ; The null hypothesis, H 0 and alternative hypothesis, H 1 will always be given in terms of p. Make sure you clearly define p before writing the hypotheses