Final answer:
The critical value for a one-mean z-test at the 10% significance level for a left-tailed test is -1.282.
Step-by-step explanation:
The critical value for a one-mean z-test at the 10% significance level for a left-tailed test is -1.282. The critical value or values can be found by referring to the z-table or using a calculator. In this case, the critical value for the 10% significance level is -1.282.