# Hypothesis Testing

Scheme of work: Year 12 A-Level: Applied: Statistics: Hypothesis Testing

#### Prerequisite Knowledge

• Use simple, discrete probability distributions, including the binomial distribution;
• Identify the discrete uniform distribution;
• Calculate probabilities using the binomial distribution.
• Calculate cumulative probabilities using the binomial distribution

#### Success Criteria

• Set up a null and alternative hypothesis based on a binomial distribution
• Understand when to use a one- or two-tailed test.
• Understand the importance of the significance level in a statistical test.
• Test an observed value of a test statistic against the significance level.
• Find a critical region or a test.

#### Teaching Points

• When setting up the null and alternative hypotheses, students often find it helpful to draw a diagram detailing the significance level, critical region and whether it is a one- or two-tailed test.

One-Tailed Test 5% significance level

Two-Tailed Test 5% significance level

• Test conclusions must be written based on the context specified in the question.
• When testing a hypothesis, students should test against the test statistic rather than finding the critical region, which often leads to errors in working.

#### Common Misconceptions

• When summarizing a hypothesis test with the correct values, some students make an incorrect conclusion or do not conclude.
• When identifying the critical region students often use incorrect notation.
• Some students write their hypothesis in words rather than H0: p = 0.5 H1 : p >  0.5.
• Students drop marks in exams through their notation; for instance, they write P(X < a) rather than P(X ≤ a)
• Some students try to find the critical region when testing a hypothesis. Unfortunately, this method requires more detailed work, often leading to errors.

## Hypotheses Testing Resources

### Mr Mathematics Blog

#### Estimating Solutions by Rounding to a Significant Figure

Explore key concepts, FAQs, and applications of estimating solutions for Key Stage 3, GCSE and IGCSE mathematics.

#### Understanding Equivalent Fractions

Explore key concepts, FAQs, and applications of equivalent fractions in Key Stage 3 mathematics.

#### Transforming Graphs Using Function Notation

Guide for teaching how to transform graphs using function notation for A-Level mathematics.