What Z-value is used for a 95% confidence level in a one-sided test?

For a one-sided test at a 95% confidence level, the Z-value corresponds to the point in the standard normal distribution where 95% of the data lies to the left. This means that only 5% of the distribution falls to the right of this point.

To find this Z-value, we look at the critical value that gives us the cumulative probability of 0.95. In standard normal distribution tables or using statistical software, the Z-value that achieves this is approximately 1.645. However, for practical purposes, this is often rounded to 1.65.

This Z-value of 1.65 represents the point where, under the normal curve, you'll find that 95% of the distribution lies to the left, making it the correct choice for a one-sided test.

In contrast, the other values given would correspond to different confidence levels or scenarios in a two-tailed test. For instance, 1.96 is applicable for a two-sided 95% confidence level, while 2.33 relates to a one-sided test at a 99% confidence level, and 2.58 is used for a two-sided 99% confidence level. Therefore, the rounding of 1.645 to