Final answer:
To construct a 79% confidence interval, you calculate the z-score that leaves 10.5% in each tail of the standard normal distribution. This will be the z-score for 89.5% to the left. The z-score obtained is the critical value zα/2 needed for your confidence interval.
Step-by-step explanation:
The student is asking to find the critical value zα/2 for constructing a 79% confidence interval. This value is critical for determining the range in which we can expect the true population parameter to lie with 79% certainty. To construct a confidence interval with a 79% confidence level, we look for the z-score that leaves a total of 21% in the tails (100% - 79%) of the standard normal distribution.
This 21% is split equally between the two tails, so each tail would contain 10.5% of the probability. Using a z-score table or calculator, we can find the z-score that corresponds to 0.895 (0.5 + 0.395) area to the left under the normal curve.
The z-score that corresponds to this area is approximately zα/2 = z0.105. This value is then used as the multiplier for the standard error in the calculation of the confidence interval.