The correct answer is: B. $t = \frac{{\overline {{x_1}} – \overline {{x_2}} }}{S}\sqrt {\frac{{{n_1} + {n_2}}}{{{n_1} – {n_2}}}} $
The formula for the t-test for the difference of two means is:
$$t = \frac{{\overline {{x_1}} – \overline {{x_2}} }}{S}\sqrt {\frac{{{n_1} + {n_2}}}{{{n_1} – {n_2}}}} $$
where:
- $\overline{{x_1}}$ is the mean of the first sample
- $\overline{{x_2}}$ is the mean of the second sample
- $S$ is the pooled standard deviation
- $n_1$ is the number of observations in the first sample
- $n_2$ is the number of observations in the second sample
The t-test is a statistical test that is used to compare the means of two groups. It is a parametric test, which means that it assumes that the data are normally distributed. The t-test can be used to test for a difference in means between two groups, or to test for a difference in means between two groups after adjusting for covariates.
The t-test is a powerful test, but it is important to note that it is sensitive to the assumption of normality. If the data are not normally distributed, the t-test may not be accurate.
The t-test is a versatile test that can be used in a variety of settings. It is a common test that is used in many fields, including statistics, psychology, and medicine.