1. T10-01 - 1 T10-01 2 Population Hypothesis Tests Purpose Allows the analyst to analyze the results of hypothesis testing of the difference of 2 population means compared to a hypothesized difference (Do) for sample means (Z equal variance), means (t equal variance), means (t unequal variance), and proportion (Z) situations based on an  significance level. The hypothesis tests include the 3 alternative options of "not equal", "greater than", and "less than" with appropriate conclusion, p-value, test statistic, and critical value(s). Inputs  levelSample mean (Xbar 1 and Xbar2) Population/Sample standard deviation (Std Dev 1 and Std Dev 2) Sample size (n1 and n2)Hypothesized difference Hypothesis alternative Outputs Test StatisticCritical Value(s) p-valueHypothesis test conclusion

2. T10-01 - 2 2 Population Hypothesis Tests - Means

3. T10-01 - 3 2 Population Hypothesis Tests - Means

4. T10-01 - 4 2 Population Hypothesis Tests - Means

5. T10-01 - 5 Means (Z Known Equal Variance) Large samples (n1 >= 30) and (n2 >= 30) Same known variance Difference of Means - Independent sampling. If these assumptions are met, the sampling distribution is approximated by the Z-distribution. Methodology Assumptions

6. T10-01 - 6 Means (Z Known Equal Variance)

7. T10-01 - 7 Example Assume Population 1 and Population 2 have known equal variance, test with  =.05 to determine if population 1 is statistically larger than population 2.

8. T10-01 - 8 Input the Population Name, signifance level (.XX for XX%), Hypothesized difference, Xbar, Std Dev, and n for both samples. The Hypothesis test results are automatically calculated Select the alternative hypothesis

9. T10-01 - 9 Populations have same unknown variance Independent sampling If these assumptions are met, the sampling distribution is approximated by the t-distribution with Methodology Assumptions Means (t Unknown Equal Variance) Pooled estimator of variance

10. T10-01 - 10 Means (t Unknown Equal Variance)

11. T10-01 - 11 Example Assume the following populations have unknown equal variance, test with  =.10 to determine if population 1 is statistically the same as population 2.

12. T10-01 - 12 Input the Population Name, signifance level (.XX for XX%), Hypothesized difference, Xbar, Std Dev, and n for both samples. The Hypothesis test results are automatically calculated Select the alternative hypothesis

13. T10-01 - 13 Populations have different unknown variance Independent sampling If these assumptions are met, the sampling distribution is approximated by the t-distribution with df=n1+n2-2. Methodology Assumptions Means (t Unknown Unequal Variance)

14. T10-01 - 14 Means (t Unknown Unequal Variance)

15. T10-01 - 15 Example Assume the following populations have unknown unequal variance, test with  =.10 to determine if population 1 is statistically the same as population 2.

16. T10-01 - 16 Input the Population Name, signifance level (.XX for XX%), Hypothesized difference, Xbar, Std Dev, and n for both samples. The Hypothesis test results are automatically calculated Select the alternative hypothesis

17. T10-01 - 17 2 Population Hypothesis Tests - Proportions

18. T10-01 - 18 2 Population Hypothesis Tests - Proportions

19. T10-01 - 19 2 Population Hypothesis Tests - Proportions

20. T10-01 - 20 Large samples (defined below) If these assumptions are met, the sampling distribution is approximated by the Z-distribution. Methodology Assumptions Proportions (Z)

21. T10-01 - 21 Proportions (Z) Because the population proportions are rarely known, we calculate a point estimator as follows Pooled estimator of proportion

22. T10-01 - 22 Proportions (Z)

23. T10-01 - 23 Difference of 2 Proportions - Example Random samples are taken from two populations, test with  =.01 to determine if population 1 is statistically the same as population 2.

24. T10-01 - 24 Input the Population Name, signifance level (.XX for XX%), Hypothesized difference, Phat and n for both samples. The Hypothesis test results are automatically calculated Select the alternative hypothesis