Which Z-value corresponds to a 99% confidence level in a two-sided test?

In statistics, the Z-value, often referred to as the critical value, corresponds to the standard normal distribution and is used to determine the boundaries for a confidence interval. For a 99% confidence level in a two-sided test, the area in the tails of the normal distribution must be 1% (0.01), split equally between the two tails. This means that there is 0.005 in each tail.

To find the Z-value that corresponds to the 99% confidence level, one would look for the value at which 99% of the data falls below it. This involves examining the standard normal distribution (Z-table) or using statistical software for the cumulative distribution function.

At the 99% confidence level, a Z-value of approximately 2.58 is required, meaning that about 2.58 standard deviations above the mean encompasses 99% of data points under the bell curve of a standard normal distribution. This Z-value ensures that the interval you calculate will accurately reflect the true population parameter with the specified confidence.

Values like 2.33, 1.96, and 1.65 do not correspond to the 99% confidence level for two-sided tests. For example, 1.96 is used