Final answer:
To find the critical value for a left-tailed t-test with a sample size of 8 and α=0.025, we calculate the degrees of freedom (7 for this case) and consult a t-distribution table for the corresponding critical value.
Step-by-step explanation:
The critical value for a left-tailed t-test for dependent samples when the sample size is 8 and α=0.025 is calculated using the t-distribution table for degrees of freedom (df).
Degrees of freedom for a dependent sample t-test are calculated as the sample size (n) minus 1.
Therefore, with a sample size of 8, we have 7 degrees of freedom (df = n - 1 = 8 - 1 = 7).
To find the critical value, we look up the value in the t-distribution table that corresponds to df = 7 and α=0.025 for a left-tailed test.
The closest value in the table of critical values is typically found in a statistics textbook or statistical software.
While the precise value depends on the specific t-distribution table or software being used, one can typically find a critical value close to options provided in multiple-choice questions.
As such, provided options need to be checked against the t-distribution table for df = 7 and α=0.025.