statistics - topic 6: hypothesis testing Flashcards
what is a hypothesis?
a hypothesis is a claim about a population parameter ie population mean or proportion
what is the null hypothesis?
it states the assumption to be tested and it always relates to a population parameter not a sample statistics
what is the alternative hypothesis?
the opposite of the null hypothesis and is generally the hypothsis that the researcher is trying to support
what is the level of significance?
The level of significance defines the critical value(s) and rejection region of the sampling distribution in which the null hypothesis is deemed unlikely to be true
what is a type 1 error in making decisions?
it occurs when a true null hypothesis is incorrectly rejected, the probability of a type 1 error is equal to the level of significance or a
what is a type 2 error in making decisions?
occurs when a false null hypothesis is not rejected, the probability of a type 2 error is 𝛽
what is the power of the test?
The power of a test is the probability of rejecting a null hypothesis that is false
what is the formula for the power of the test?
𝑃𝑜𝑤𝑒𝑟=( 1−𝛽 ) = 𝑃(𝑅𝑒𝑗𝑒𝑐𝑡 𝐻_0 |𝐻_0 𝑖𝑠 𝑓𝑎𝑙𝑠𝑒)
what is the relationship between the power of the test and the sample size?
The power of the test increases as the sample size increases
what are the two ways which a hypothesis test can be done?
a critical value approach and a p value approach
what are the possible alternative hypothesizes for the two tail test?
the population mean is not equal to the sample mean
what is the possible alternative hypothesis for the one tail test?
it is either bigger than the mean or smaller then the mean
what are the decisions rules?
The decision rule is:
If 𝑝-value < a , reject 𝐻_0
If 𝑝-value ≥ a, do not reject 𝐻_0
