The answer depends on the distribution. But since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.
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A z-value by itself, has nothing to do with level of confidence.A z-value can be used to calculate probabilities of observing a result that is at least as far from the mean. That probability measure can be used to calculate the level of confidence but you need to be careful about using the one-tailed or two-tailed measures - as appropriate.A z-value by itself, has nothing to do with level of confidence.A z-value can be used to calculate probabilities of observing a result that is at least as far from the mean. That probability measure can be used to calculate the level of confidence but you need to be careful about using the one-tailed or two-tailed measures - as appropriate.A z-value by itself, has nothing to do with level of confidence.A z-value can be used to calculate probabilities of observing a result that is at least as far from the mean. That probability measure can be used to calculate the level of confidence but you need to be careful about using the one-tailed or two-tailed measures - as appropriate.A z-value by itself, has nothing to do with level of confidence.A z-value can be used to calculate probabilities of observing a result that is at least as far from the mean. That probability measure can be used to calculate the level of confidence but you need to be careful about using the one-tailed or two-tailed measures - as appropriate.
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The choice of one-tailed or two-tailed tests follows the logic of the hypothesis that is being tested! The one-tailed test, if appropriate, will be more powerful.
The type I error is 0.0027 only when a two tailed test is used with a z-score of ±3. There are many occasions when a one-tailed test is more appropriate and with the same test would have half the Type I error. Furthermore, it is more usual for the researcher to specify the type I error first - 0.05, 0.01 or 0.001 are favourites - and to select one-or two-tailed critical region after that. It is, therefore, more likely that the Type I error is a "round" number (5%, 1% or 0.1%) while the critical z-score is not.
no tail