APPLIED MATHS HYPOTHESIS TESTING

Chapter 7

Population parameter

The probability, p, in a binomial distribution

Hypothesis

A statement made about the value of a population parameter

Hypothesis test

Uses a sample or experiment to determine whether or not to reject the hypothesis

Null hypothesis, H₀

The hypothesis we assume to be correct (i.e. the probability is unchanged)

Alternative hypothesis, H₁

Tells you about the population parameter if your assumption is show to be wrong (i.e. the probability is different)

Test statistic

The result of the experiment or statistic calculated from the sample. E.g. how many times you roll a 6. In a hypothesis test, you consider how likely this is to occur

Significance level

The threshold at which we reject H₀. If the probability of the test statistic is less than the given significance level, it is so unlikely that our population parameter, p, must be different from the assumption, so we reject H₀ and accept H₁

In a one tail test, the inequality sign will be the same way round as the inequality sign in...

H₁

Two tailed test

When H₁ states p ≠ rather than p > or p <. Split the significance level between the two tails

Critical region

The range of values of the test statistic that would lead to you rejecting H₀

Critical values

The first value that falls in the critical region, being on the boundary of the critical region

Actual significance level

The probability of being in the critical region. The same as the probability of incorrectly rejecting H₀