Final answer:
The z* critical value for constructing a confidence interval for one proportion at different confidence levels is 1.645 for 90% confidence, 1.96 for 95% confidence, and 2.576 for 99% confidence.
Step-by-step explanation:
To construct a confidence interval for one proportion, we need to determine the critical value (z*) at different confidence levels. The z* critical value for a 90% confidence level is 1.645, for a 95% confidence level is 1.96, and for a 99% confidence level is 2.576. These critical values can be found in the standard normal probability distribution table.