What Z-value is used for a 99% confidence level in a one-sided test?

The Z-value for a one-sided test at a 99% confidence level corresponds to the value that captures the upper 1% of the standard normal distribution. In statistical terms, for a confidence level of 99%, the remaining area in the tail (to the right) is 1%, or 0.01, which means we want to find the Z-value where the cumulative probability is 0.99.

In the standard normal distribution, a Z-value of approximately 2.33 gives a cumulative probability very close to 0.99. This is derived from Z-tables or normal distribution calculators, which are standard tools used in statistics.

Using a Z-value of 2.33 means that when we are looking for the value above which only 1% of the data falls, that value corresponds to our one-sided test at a confidence level of 99%. This level is crucial in risk management for ensuring that extreme outcomes (which represent unfavorable events) are considered within the context of the overall risk assessment.

The other Z-values correspond to different confidence levels: 1.96 is for 95%, 1.65 is for around 90%, and 2.58 is for approximately 99% in a two-sided