# Two-sample t test

The two-sample t-test is a fundamental statistical method used to compare the means of two independent groups to determine if there is a significant difference between them. It is a powerful tool in various fields, including psychology, biology, and economics, enabling researchers to assess the impact of interventions, treatments, or variables on different populations. By analyzing the means and variances of two samples, the t-test provides valuable insights into whether observed differences are statistically significant or simply due to chance. Understanding its principles and applications is crucial for researchers and practitioners seeking to draw valid conclusions from their data.

- What is a pooled variance?
- What does Welch's t-test measure?
- What conditions must be met for conducting a two-sample t test for the means?
- What is the difference between using the pooled variance and the unpooled variance in a two-sample t test for means?
- What is the mathematical formula for the pooled variance of two populations?
- Can a two-sample t-test be used if the samples are of a different size?
- Can a two-sample t-test be used if the samples have different variances?
- How do you adjust a two-sample t-test to accomodate samples of different sizes?
- When is Welch's t-test used?
- How are two-sample t-tests different from two sample z-tests?
- How do you find the P value for a two tailed test with n=21 and test statistic t =1.557?
- What is a paired and unpaired t-test? What are the differences?
- How do you find a p value if n = 10 for a two-tailed test, and the test statistic t = 2.52?
- Why is a pooled standard deviation used for a two sample t-test?