Tutorial Exercise Use the information provided to answer the questions. Population 1 2 Sample Size 18 11 Sample Mean 34.8 32.4 Sample Variance 4.1 5.5 State the null and alternative hypotheses for testing for a significant difference in means. Calculate the pooled estimate of , the associated degrees of freedom, and the observed value of the t statistic. What is the rejection region using = 0.05? What can be said about the p-value for the test? What can you conclude from these data? Step 1 = 0 X Recall that the null hypothesis Ho for the difference between two means is Ho: ( - ) = Do, where and are the means for populations 1 and 2, respectively, and Do is the specifi difference between means. We are asked to test for a difference between means, so the null hypothesis should state that there is no difference between means, or D = Therefore, the null hypothesis is Ho: (1 - 2) = The alternative hypothesis H is that there is a difference between means. This can be written as H: ( - 2) ? 0.