The critical z score value for an 80% confidence level is approximately ±1.28.
To understand why this is the case, we look at the concept of confidence intervals in statistics. A confidence level of 80% means that we are willing to accept a 20% chance that the true population parameter lies outside our interval.
Since confidence intervals are typically derived from the standard normal distribution, we can find the critical z score that corresponds to the middle 80% of the distribution. This leaves 10% in each tail because the normal distribution is symmetric.
Using a standard normal distribution table or a calculator, we find the z score that corresponds to a cumulative probability of 0.90 (which is the sum of the 80% confidence level and the 10% in the upper tail). This yields a z score of approximately 1.28. Thus, the critical z scores for an 80% confidence interval are -1.28 and +1.28.