S2- Hypothesis Testing Flashcards
What is a population?
A collection of items
What is a sampling frame?
A list of items in a population
What is a census?
A complete enumeration of a population
What is a sample?
A selection of items from a population
What is a statistic?
A random variable that consists of data from just the sample
What is the null hypothesis (H0)?
The working hypothesis, which is assumed to be true
What is the alternative hypothesis (H1)?
One of the hypotheses that could describe the situation if H0 isn’t true
What is a test statistic?
A statistic used in a hypothesis test
What is a sampling distribution?
The distribution of a statistic
What is the critical region?
The range of values that would lead you to reject the null hypothesis
What is the significance level?
The level of probability we are prepared to accept- used to determine the critical region.
What values does the significance level normally take in S2?
5% or 10%
When is the test one-tailed?
when H1 is either ≥ or ≤ than p (if binomial) or λ (if Poisson)
When is the test two-tailed?
when H1 is ≠ to p (if binomial) or λ (if Poisson)
What happens to the significance level with a two-tailed test?
It gets halved, with half the significance level determining the lower critical region, and the other half the upper critical region
When do you accept H0?
If P(X≥x) or P(X≤x) (depending on what the question asks) is more than the significance level
When do you accept H1?
If P(X≥x) or P(X≤x) (depending on what the question asks) is less than the significance level
Advantages of taking a census
Every member of the population is used.
It is unbiased.
It gives an accurate answer.
Disadvantages of censuses
It takes a long time.
It is costly.
It is often difficult to ensure that the whole population is surveyed.
Advantages of sampling
Sample will be representative if population large and well mixed.
Usually cheaper.
Essential if testing involves destruction (life of a light bulb, etc.).
Data usually more easily available.
Disadvantages of sampling
Uncertainty, due to the natural variation – two samples are unlikely to give the same result.
Uncertainty due to bias prevents the sample from giving a representative picture of the population
