T T 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

T Population Hypothesis Tests - Means

T Population Hypothesis Tests - Means

T Population Hypothesis Tests - Means

T 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

T Means (Z Known Equal Variance)

T 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.

T 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

T 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

T Means (t Unknown Equal Variance)

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

T 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

T 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)

T Means (t Unknown Unequal Variance)

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

T 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

T Population Hypothesis Tests - Proportions

T Population Hypothesis Tests - Proportions

T Population Hypothesis Tests - Proportions

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

T Proportions (Z) Because the population proportions are rarely known, we calculate a point estimator as follows Pooled estimator of proportion

T Proportions (Z)

T 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.

T 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