1. The problem: Understanding when to use one-sample or two-sample t-tests. 2. One-sample t-test is used when you want to compare the mean of a single sample to a known population mean. The formula is: $$t = \frac{\bar{x} - \mu}{s / \sqrt{n}}$$ where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size. 3. Two-sample t-test is used when you want to compare the means of two independent samples to see if they differ significantly. The formula (for equal variances) is: $$t = \frac{\bar{x}_1 - \bar{x}_2}{s_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$$ where $\bar{x}_1, \bar{x}_2$ are sample means, $n_1, n_2$ are sample sizes, and $s_p$ is the pooled standard deviation. 4. Important rules: - Use one-sample t-test when comparing one sample mean to a known value. - Use two-sample t-test when comparing two independent sample means. - Ensure samples are independent and approximately normally distributed. 5. Summary: If you have one group and a known population mean, use one-sample t-test. If you have two groups and want to compare their means, use two-sample t-test.