Final answer:
To construct an 83% confidence interval, the critical value zα/2 is approximately 1.37, found by using a z-table to look up the area corresponding to α/2, which is the tail probability for one side of the distribution.
Step-by-step explanation:
The question is asking to find the critical value zα/2 for an 83% confidence interval. This critical value is needed to calculate the range of values within which we can be confident that our population parameter lies. To find this value, we first need to determine α, which is the complement of the confidence level. For an 83% confidence interval, α = 1 - 0.83 = 0.17. Since we are constructing a two-tailed confidence interval, α/2 = 0.17/2 = 0.085. We then look up this α/2 value in a standard normal z-table to find the corresponding z-score that has an area to the right of 0.085, which is also the needed critical value zα/2.
Using a z-table or statistical software, we find that the critical value zα/2 required for an 83% confidence interval is approximately zα/2 ≈ 1.37. This means that we must go out 1.37 standard deviations on either side of the calculated sample mean to capture the central 83 percent of the probability distribution.