1. **Problem Statement:** Determine which of the given statements about the t statistic and standard errors are FALSE. 2. **Evaluate Each Statement:** - Statement 1: "When computing the t statistic, the denominator is sample variance" - The formula for the t statistic is $$t=\frac{\bar{x} - \mu}{SE}$$ where $$SE=\frac{s}{\sqrt{n}}$$ and $$s^2$$ is the sample variance. - The denominator is the estimated standard error, not the sample variance. - **This statement is FALSE.** - Statement 2: "Everything else being equal, smaller estimated standard errors will produce larger t-statistic values" - Since $$t=\frac{\bar{x} - \mu}{SE}$$, if $$SE$$ is smaller, $$t$$ is larger. - **This statement is TRUE.** - Statement 3: "Everything else being equal, smaller samples tend to have larger estimated standard error" - $$SE=\frac{s}{\sqrt{n}}$$, so smaller $$n$$ leads to larger $$SE$$. - **This statement is TRUE.** - Statement 4: "If two separate samples have the same mean but different standard errors, it is necessarily the case that the larger sample more likely result in a rejection of the null hypothesis" - Larger sample usually means smaller $$SE$$, but rejection depends on $$t$$ statistic and critical value. - Without knowing other factors or actual $$t$$ values and variance, this is not necessarily true. - **This statement is FALSE.** - Statement 5: "Everything else being equal, if a sample has a large amount of variance, the estimated standard error will also be large" - $$SE=\frac{s}{\sqrt{n}}$$, and variance $$s^2$$ relates directly to $$s$$. - Larger variance yields larger $$s$$ and thus larger $$SE$$. - **This statement is TRUE.** 3. **Final Answer:** The FALSE statements are: - Statement 1 - Statement 4 Therefore, the FALSE statements are: **1. When computing the t statistic, the denominator is sample variance** **4. If two separate samples have the same mean but different standard errors, it is necessarily the case that the larger sample more likely result in a rejection of the null hypothesis**