Two-sample separate variance t-test for difference of population means
Why? To compare two unknown population means, μ1 and μ2.
When? The following conditions must be present for the test to be accurate and valid. Conditions 2, 3, and 4 may have to be assumed to proceed with the test.
1. σ1 and σ2 are unknown.
2. The samples are selected randomly.
3. The samples are selected independently.
4. The samples come from normally distributed populations.
How:
Preliminary: • Select the level of significance, α (use 0.05 unless otherwise stated).
• Define the parameters μ1 and μ2 in the context of the populations being studied.
1. State the null hypothesis: H0: μ1 = μ2
Choose an alternative hypothesis from one of the following:
(i.) H1: μ1 > μ2 (ii.) H1: μ1 < μ2 (iii.) H1: μ1 [pic] μ2
2. Calculate the test statistic:
[pic]
3. Find the P-value (observed significance level): each case corresponds to the alternative hypotheses listed above; use t distribution with degrees of freedom equal to the smaller of n1-1and n2-1.
(i.)[pic] (ii.)[pic] (iii.)[pic]
[pic] [pic] [pic]
[pic] [pic] [pic] [pic]
4. Conclusion: Reject H0 if the P-value is less than the level of significance; otherwise, do not reject H0. Write a conclusion in statistical terms as well as a practical conclusion in the context of the problem. The practical conclusion should always be stated in terms of the alternative hypothesis. When H0 is rejected the result is “statistically significant.”
Two-sample separate variance t-interval for μ1-μ2
Why? To locate the difference between two population means μ1 - μ2.
When? Under the same conditions as for the t-test listed above.
How:
[pic]
where [pic] is the critical value from the t distribution corresponding to level C confidence and degrees of freedom equal to the smaller of n1-1and n2-1.
