6-2 tests of significance 6.2. Tests of significance
1. vocabulary
a. Null hypothesis Ho
b. Alternative hypothesis Ha: the claim that we are trying to find evidence for
c. P-value: small P-values provide evidence against Ho
(1) quantifies the probability of getting an outcome as extreme or more extreme than the
actually observed outcome
(2) “extreme” in relation to being consistent with Ha and inconsistent with Ho
2. stating hypotheses
a. one-sided vs two-sided alternative
b. always use parameter in hypotheses
3. P-value and statistical significance
a. statistical significance level (α) is the maximum level that a manager will allow the Pvalue to be and still reject Ho
b. “significant” does NOT mean “important”, rather “not likely to happen by chance”
4. test for a population mean
(1) state the hypotheses
(2) calculate the test statistic
(3) find the P-value
5. tests with a fixed significance level
a. upper p critical value z* corresponds to common values of α
b. Reject Ho at significance level α for three possible cases of z*
(1) Ha:&micro;&gt;&micro;o if z≥z*
(2) Ha:&micro;&lt;&micro;o if z≤-z*
(Example 6.15, p 334)
(3) Ha:&micro;≠&micro;o if |z|≥z*, where z* is the upper α/2 critical value from Table C
(Example 6.16, p 335)
6. tests from confidence intervals
a. a level α two-sided test rejects a hypothesis Ho:&micro;=&micro;o when the value of &micro;o is outside a
level 1-α confidence interval for &micro;