Final answer:
The critical value for a left-tailed test can be found by comparing the test statistic to the critical value. In this case, the critical value is -2.33.
Step-by-step explanation:
To find the critical value(s) for a left-tailed test with a test statistic of z = -1.71 and a significance level of 0.01, we need to compare the test statistic to the critical value. The critical value is the value that separates the region of rejection from the region of non-rejection. Since this is a one-tailed test, there is only one critical value.
Using the provided information, the critical z-value for a significance level of 0.01 is -2.33. Therefore, the correct choice is A. There is one critical value; the critical value is -2.33.