T Test Groups
1. The problem asks for t-tests for four groups labeled a, b, c, and d.
2. A t-test compares means of two groups to see if they are significantly different.
3. To perform t-tests, we need numeric data values for each group (a, b, c, d).
4. Calculate sample means and sample standard deviations for each group.
5. Use the formula for the t-statistic:
$$ t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} $$
where $\bar{x}$ is the sample mean, $s^2$ is the sample variance, and $n$ is sample size.
6. Determine degrees of freedom and compare t-statistic to critical values for significance.
7. Without specific data or hypotheses, detailed t-values and conclusions cannot be calculated.
8. Please provide the numeric data or specify which groups you want compared.