The image shows the following values:

$\bar{X}_1 = 5.8$ $\bar{X}_2 = 10.1$ $n_1 = n_2 = 30$

These appear to be sample means ($\bar{X}_1$ and $\bar{X}_2$) and sample sizes ($n_1$ and $n_2$) for two groups. To calculate the t-test value, you'll need to know the standard deviations (or variances) of the two groups. If you have this information, you can use it to calculate the t-test statistic.

If the standard deviations are not given, it might be assumed that they are equal, leading to a pooled t-test. The formula for the t-test statistic in this case would be:

$t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{s_p^2 \left(\frac{1}{n_1} + \frac{1}{n_2}\right)}}$

Where:

$s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}$

is the pooled variance, and $s_1^2$ and $s_2^2$ are the sample variances.

If the standard deviations or variances are not provided, we cannot calculate the exact t-test value. Do you have the variances or standard deviations for these samples?

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Would you like further details or have any questions? Here are five related questions you might consider:

1. What is the difference between a pooled t-test and a Welch's t-test?
2. How do you calculate the degrees of freedom for a t-test?
3. What assumptions are required for the t-test to be valid?
4. How can you interpret the p-value obtained from a t-test?
5. How would you calculate a confidence interval for the difference in means?

Tip: Always check the assumptions of normality and equal variances when using a t-test, as violations can affect the accuracy of the results.