5. Practice finding the critical t-values (using the t-table) for the following:

1. A 95% confidence interval based on n=15 observations
2. A 95% confidence interval from a random sample of 28 observations
3. A 90% confidence interval from a sample size of 28

6. What do statisticians mean when they discuss the robustness of a test? Is a one-sample t-test robust? Is a two-sample t-test robust?

7. A 95% confidence interval for the difference between two means is reported as (0.8, 2.3), what can you conclude about the results of the significance test of the null hypothesis that the population means are equal versus the two-sided alternative? Will larger samples generally give a larger or smaller margin of error for the difference between two sample means?

8. A significance test comparing two means gave t=-1.97 with 10 degrees of freedom. Can you reject the null hypothesis that the means are equal versus the two-sided alternative at the 5% significance level? Can you reject the null hypothesis that the means are equal versus the one-sided alternative that the difference between means is negative?