To determine the P-value for a left-tailed test with n = 38 and a test statistic of t = 2.714, we first need to find the degrees of freedom. For a t-test, the degrees of freedom (df) is calculated as:
\[ df = n - 1 = 38 - 1 = 37 \]
Next, we can use Table A-3 (which is likely a t-distribution table) to find the range of P-values corresponding to a test statistic of t = 2.714 with 37 degrees of freedom.
In a left-tailed test, we are interested in the area to the left of the test statistic. However, since our test statistic is positive (2.714), we will actually be looking for the right tail (1 - P-value) as the table typically provides information for negative t-values (or right-tail probabilities).
Without access to specific values from Table A-3, we can estimate that a t-value of 2.714 with 37 degrees of freedom is likely to have a P-value less than 0.01 but greater than 0.005 based on common critical values.
Thus, the most likely conclusion is:
C) 0.005 < P-value < 0.01.
Please verify this with the actual Table A-3 to ensure accuracy.