Final answer:
To find the critical value for a left-tailed test with α = .10, refer to a z-table to locate the z-score that places 0.10 in the tail. The critical value is approximately -1.2816.
Step-by-step explanation:
You are performing a left-tailed test with a sample size of 65, and have been asked to find the critical value given that the level of significance (α) is .10. To find the critical value for a left-tailed test, you will refer to a z-table that incorporates the standard normal distribution. The critical value is the z-score that corresponds to the cumulative probability of α. Since α = .10, you look up the value in the z-table that has 0.10 in the left tail.
The z-score you find will be negative because it's on the left side of the normal distribution, which represents values below the mean. A z-score of approximately -1.2816 would have 0.10 to its left according to the z-table, which is the critical value for this specific left-tailed test. Hence, -1.2816 is the critical value to four decimal places.