Answer:

Task 1: As the sample size (n) increases, the values of t tend to approach the values of the standard normal distribution (Z-distribution) for larger sample sizes. In other words, the values of t become closer to the critical values of the Z-distribution as n increases. This happens because as the sample size increases, the t-distribution approximates the standard normal distribution more accurately.Task 2: For n = 0, we cannot compute the t-value because the t-distribution requires a non-zero sample size. The formula for the t-value involves the square root of n, and if n = 0, the denominator becomes zero, which is undefined in mathematics.In-Class Activity 2:To find the confidence coefficients for each of the given situations, we need to refer to the t-distribution table or use statistical software. The confidence coefficient represents the area under the t-distribution curve that corresponds to the specified confidence level.1. n = 6, 90% confidence:The confidence coefficient for a 90% confidence level with 6 degrees of freedom is approximately 1.943.2. n = 7, 90% confidence:The confidence coefficient for a 90% confidence level with 7 degrees of freedom is approximately 1.895.3. n = 12, 95% confidence:The confidence coefficient for a 95% confidence level with 12 degrees of freedom is approximately 2.179.4. n = 17, 95% confidence:The confidence coefficient for a 95% confidence level with 17 degrees of freedom is approximately 2.110.5. n = 24, 99% confidence:The confidence coefficient for a 99% confidence level with 24 degrees of freedom is approximately 2.797.6. n = 8, 99% confidence:The confidence coefficient for a 99% confidence level with 8 degrees of freedom is approximately 3.355.7. n = 10, 99% confidence:The confidence coefficient for a 99% confidence level with 10 degrees of freedom is approximately 3.169.These values can be used to determine the critical region or margin of error associated with the specified confidence levels and sample sizes in various statistical calculations