BSB123 Lecture Notes - Lecture 7: Random Variable, Null Hypothesis, Alternative Hypothesis
Hypothesis Testing
Part 1
- Testing of the mean
oMake inference about the hypothesised value of the population mean
- A statistical method of determining the strength of evidence against the hypothesised value
of a parameter of interest
- Finds out the presence/absence of:
oA condition
oAn effect
oA change/difference
oA relationship
- Null hypothesis (H0) – hypothesis of no change
- Alternative hypothesis (H1) – hypothesis of change/action
- Objective is to collect evidence to determine whether or not we reject H0
- Type 1 error (false positive)
oDetecting an effect/condition that is not present
- Type 2 error (false negative)
oFailure to detect an effect/condition that is present
- p-value
oThe probability of obtaining the observed sample result or more extreme when the
null hypothesis is indeed true (probability of making a type 1 error)
oWhen p-value = <1% - very strong evidence against H0
oWhen p-value = 1% - 5% - strong evidence
oWhen p-value = 5% - 10% - weak evidence
oWhen p-value = >10% - no evidence
- Whether or not the H0 is rejected depends on the max type 1 risk willing to be taken
oGenerally, 1%
- Hypothesis test for the known population with a known standard deviation – z test
- One and two tail tests
oOne tail tests include upper and lower tail. Occur when the question is to find out
whether something is greater/lesser than the mean
E.g. if the H0 = mean = 15
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Document Summary
Testing of the mean: make inference about the hypothesised value of the population mean. A statistical method of determining the strength of evidence against the hypothesised value of a parameter of interest. Finds out the presence/absence of: a condition, an effect, a change/difference, a relationship. Null hypothesis (h0) hypothesis of no change. Objective is to collect evidence to determine whether or not we reject h0. Type 1 error (false positive: detecting an effect/condition that is not present. Whether or not the h0 is rejected depends on the max type 1 risk willing to be taken: generally, 1% Hypothesis test for the known population with a known standard deviation z test. One and two tail tests: one tail tests include upper and lower tail. Occur when the question is to find out whether something is greater/lesser than the mean. Upper tail test h1 = mean > 15.
