Final answer:
The correct answer is D. -2.896, which is the t-value for which the area to the left is 0.01 with 8 degrees of freedom, as obtained from a t-distribution table or statistical calculator function.
Step-by-step explanation:
The question provided asks us to find the t-value such that the area to the left of the t-value is 0.01 with 8 degrees of freedom. This type of problem involves using either a t-distribution table or a calculator to determine the critical value for a given left-tail probability with specific degrees of freedom. In this case, since the left-tail probability (area to the left) is 0.01 and the degrees of freedom are 8, we must look for the value corresponding to the 99th percentile (100%-1%) in a t-distribution table for 8 degrees of freedom or use a statistical calculator function such as 'invT' for inverse t-distribution.
Based on standard t-distribution tables or calculator outputs, the correct t-value that satisfies the condition mentioned is -2.896 (Option D). Positive t-values correspond to areas to the right of the mean in the t-distribution, while negative t-values correspond to areas to the left of the mean. Therefore, B. -4.501 represents a more extreme value on the left and A. 2.896 represents a value on the right.