Final answer:
The question asks for the approximations Tn, Mn, and Sn for n = 6 and 12, and the corresponding errors ET, EM, and ES. Without the exact function or data, it is not possible to compute these values. In a broader context, these concepts relate to statistical analysis and numerical integration methods.
Step-by-step explanation:
To approximate Tn, Mn, and Sn for n = 6 and 12, we need additional information such as the function we are approximating or the statistical data we are analyzing. These approximations usually represent the trapezoidal, midpoint, and Simpson's rules for numerical integration, or they could be related to statistical measurements depending on the context. Without this context, we cannot provide the approximations or calculate the corresponding errors ET, EM, and ES.
For statistical analysis, when both sample sizes are five or larger, the Student's t approximation for the t-distribution is considered very good. It is important to note that if variances are to be used, they should not be pooled unless specified. Standard deviation is a statistical measure of the dispersion of a set of values, and n typically represents the sample size.
For computations involving the t-distribution or statistical tests, it's common to use a calculator, a table of values, or computer software to find the critical value ta for a given significance level a. The process typically involves inputting the sample means, standard deviations, and sample sizes into a statistical function to obtain the result.
The sum of squared errors (SSE) and the standard deviation can be calculated from the given data using statistical formulas.