# Hypothesis Testing

**AS Level**

- Understand and apply the language of statistical hypothesis testing, developed through a binomial model: null hypothesis, alternative hypothesis, significance level, test statistic, 1-tail test, 2-tail test, critical value, critical region, acceptance region, p-value
- Conduct a statistical hypothesis test for the proportion in the binomial distribution and interpret the results in context
- Understand that a sample is being used to make an inference about the population and appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis

**A Level**

- extend to correlation coefficients as measures of how close data points lie to a straight line and be able to interpret a given correlation coefficient using a given p-value or critical value (calculation of correlation coefficients is excluded)
- Conduct a statistical hypothesis test for the mean of a Normal distribution with known, given or assumed variance and interpret the results in context

### Hypothesis Testing

This resource from the Continuing Mathematics project is made up of three units covering hypothesis testing.

The second unit covers the Binomial Test and the objectives for the unit are that students will learn to write down a suitable Null Hypothesis for the symmetrical binomial situation and an Alternative Hypothesis, and be able to distinguish between and utilise one-tailed and two-tailed binomial tests.

### Successful HE Students

This Nuffield Foundation resource enables students to carry out significance tests on proportions and test hypotheses about successful applicants to higher education.

The data provided on information sheet A is simulated but similar to real data available on the UCAS website.

Information sheet B outlines the method for carrying out a significance test on a proportion and provides a worked example.

Information sheet C outlines the method for carrying out a significance test on the difference between two proportions and gives a worked example.

The same methods and examples are also given in the slideshow.

### Sampling and Hypothesis Testing: Significance Levels

Students are presented with a coin which is suspected of being biased. A hypothesis test is set up.

A results table is shown giving the significance of the result at different levels of significance for different outcomes. Students are encouraged to use the accompanying spreadsheet to explore other situations.

### Sampling and Hypothesis Testing using the Normal Distribution: Sampling

In this activity, students are given 100 natural numbers, all with value less than one hundred, and are asked to estimate the mean of the population by taking a number of samples, finding the mean of each sample and then finding the mean of the sample means.

This resource is part of the Making Stats Vital collection from Jonny Griffiths.

### Sampling and Hypothesis Testing using the Normal Distribution: Sample Mean Gap-Filler

In this activity, students are given a variety of normal distributions each containing missing numbers. Students are required to fit the given numbers into the correct place. This puzzle is designed to test students’ understanding of the mean and variance of the sample mean for a Normal distribution. A certain amount of number theory is required to find the unique answer. The resource contains an answer sheet and a set of teacher notes.

This resource is part of the Making Stats Vital collection from Jonny Griffiths.

### Geography - Hydraulic Radius

This MEI activity provides an example of hypothesis testing used in Geography.

The PowerPoint "Spearman's Rank" provides a clear introduction to hypothesis testing, null and alternative hypotheses, critical values and 1-tailed and 2-tailed tests.

The Excel spreadsheets could be used to allow students to explore calculation of correlation coefficients for small sets of data but this is beyond the A level syllabus.

### Psychology - Correlation Study

This MEI activity allows students to explore the correlation coefficient for samples of data using a given Excel spreadsheet.

Statistical Inference looks for evidence of what is happening in the population by looking at a sample. Different samples from the same population can give different results. The smaller sample size can show shows different values both positive and negative and sometimes quite high magnitudes.

Mathematical There is an experiment which is best done in a lesson before the results are analysed.

The teachers' notes are written to be suitable for teachers of either mathematics or psychology.

### Practical Statistics

Chapter 9 (pdf page 172) deals with hypotheses testing when mean and variance are given. Critical regions critical values and p values are explained. From pdf page 180 there is a more formalised procedure for hypotheses testing.

Chapter 10 (pdf page 185) deals with hypotheses testing of a large sample. Null Hypotheses, and significance levels are dealt with in examples of a practical. Pdf page 190 shows an example of binomial probabilities and the binomial distribution.