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T Test Groups

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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.