CHAPTER 7 - Hypothesis testing
1. P-test Approach
Hypothesis testing=used to test certain statements about a population based on a sample data.
Procedure:
-state hypotheses
-set criteria for a decision
-collect sample data and compute test statistic
-calc p-value
-make a decision
Z-test=any statistical test for which the distribution of the test statistic is assumed to be normally
distributed (approximately); uses sample data to test hypotheses about an unknown population
mean.
Hypothesis=expectation/prediction about a population characteristic
-there are 2 hypotheses: null and alternative (they are mutually exclusive/DISJUNCT=> cannot
overlap in any predictions)
Null hypothesis (H0)=zero effect; hypothesis you are trying to disprove (prove it is false)
Null hypothesis is rejected (should only be rejected if it is highly unlikely to be true given
the sample data)
Null hypothesis is not rejected (doesn’t mean the hypothesis is accepted, but it means that
there isn’t enough evidence to reject it)
!! it cannot be accepted anyhow
Alternative hypothesis (Ha)= predicts that there is an effect; hypothesis you suspect to be true
-it is accepted only if the null hypothesis is rejected
Two-tailed test- no specific prediction about the directiom
H0: µ= µ0
Ha: µ≠ µ0
One-tailed test-if we suspect a specific direction
o Left-tailed: population parameter is less than a particular value
H0: µ>=µ0
, Ha: µ< µ0
o Right-tailed: population parameter is greater than a particular value
H0: µ=<µ0
Ha: µ> µ0
Significance level (α)= probability threshold that determines how unlikely a sample
statistic has to be in order for the null hypothesis to be rejected.
Critical region=range of values of the sample statistic that will lead to the rejection of the
null hypothesis
Critical values= boundary values of the critical region
OBS: decreasing significance level => smaller range of values that will lead to rejection
of the null hypothesis
Increasing significance level => larger range of values that will lead to rejection of
the null hypothesis
For a two-tailed test: critical region is split equally between the 2 tails
For a left-tailed test: critical region is on the left tail entirely
For a right-tailed test: critical region is on the right tail entirely
OBS: a smaller α should be used for a two-tailed test than for a one-tailed test
Test statistic= single numerical value; difference between observed sample data and what you
expect to observe if the null hypothesis theory is true (larger test statistic=>stronger evidence
against the null hypothesis being tested); ratio: obtained difference/expected difference.
In a Z-test: test statistic=Z-statistic
P-value=probability of observing a test statistic equal to or more extreme than what was actually
observed (when H0 is assumed to be true); IT IS NOT THE PROBABILITY THAT H0 IS
FALSE (status of H0 is non-random)
1. P-test Approach
Hypothesis testing=used to test certain statements about a population based on a sample data.
Procedure:
-state hypotheses
-set criteria for a decision
-collect sample data and compute test statistic
-calc p-value
-make a decision
Z-test=any statistical test for which the distribution of the test statistic is assumed to be normally
distributed (approximately); uses sample data to test hypotheses about an unknown population
mean.
Hypothesis=expectation/prediction about a population characteristic
-there are 2 hypotheses: null and alternative (they are mutually exclusive/DISJUNCT=> cannot
overlap in any predictions)
Null hypothesis (H0)=zero effect; hypothesis you are trying to disprove (prove it is false)
Null hypothesis is rejected (should only be rejected if it is highly unlikely to be true given
the sample data)
Null hypothesis is not rejected (doesn’t mean the hypothesis is accepted, but it means that
there isn’t enough evidence to reject it)
!! it cannot be accepted anyhow
Alternative hypothesis (Ha)= predicts that there is an effect; hypothesis you suspect to be true
-it is accepted only if the null hypothesis is rejected
Two-tailed test- no specific prediction about the directiom
H0: µ= µ0
Ha: µ≠ µ0
One-tailed test-if we suspect a specific direction
o Left-tailed: population parameter is less than a particular value
H0: µ>=µ0
, Ha: µ< µ0
o Right-tailed: population parameter is greater than a particular value
H0: µ=<µ0
Ha: µ> µ0
Significance level (α)= probability threshold that determines how unlikely a sample
statistic has to be in order for the null hypothesis to be rejected.
Critical region=range of values of the sample statistic that will lead to the rejection of the
null hypothesis
Critical values= boundary values of the critical region
OBS: decreasing significance level => smaller range of values that will lead to rejection
of the null hypothesis
Increasing significance level => larger range of values that will lead to rejection of
the null hypothesis
For a two-tailed test: critical region is split equally between the 2 tails
For a left-tailed test: critical region is on the left tail entirely
For a right-tailed test: critical region is on the right tail entirely
OBS: a smaller α should be used for a two-tailed test than for a one-tailed test
Test statistic= single numerical value; difference between observed sample data and what you
expect to observe if the null hypothesis theory is true (larger test statistic=>stronger evidence
against the null hypothesis being tested); ratio: obtained difference/expected difference.
In a Z-test: test statistic=Z-statistic
P-value=probability of observing a test statistic equal to or more extreme than what was actually
observed (when H0 is assumed to be true); IT IS NOT THE PROBABILITY THAT H0 IS
FALSE (status of H0 is non-random)
