16 Hypothesis Testing Flashcards
What does hypothesis testing do?
It allows us to evaluate claims made about a population
Null hypothesis
H0, we assume that the claim made is correct
Alternative hypothesis
H1, it says the claim made is wrong
Two sided alternative
Where the alternative hypothesis is simply that the null hypothesis isn’t true
One sided alternative
Where the alternative hypothesis says that the mean is either greater than or smaller than the claim
How do we determine if the difference between an estimator and the population parameter is big or small?
We construct a test statistic (T) which has a known sampling distribution when H0 is true and some other distribution if H1 is true
Type 1 error
Falsely rejecting the null hypothesis when it is true
What is the probability of making a type 1 error?
It is equal to the significance level
Type 2 error
Failing to reject the null hypothesis when the alternative is true
Critical value
If the null hypothesis is true than the probability of getting a value larger than the critical value is equal to the significance level
When do we reject the null hypothesis for a two sided test?
When the magnitude of T is greater than the critical value
Power of the test
The probability of correctly rejecting Ho
How do you work out the power of the test?
Power= 1-P(type 2 error)
How can we increase the power of a test?
Increase the sample size
Increase the difference between the population parameter and the specified value
P value
The probability of obtaining a result that is more extreme than what was actually observed, when the hypothesis is true
