Final answer:
To construct a 98.9% confidence interval, the critical value zα/2 needed is approximately 2.576, which is found by identifying the z-score that leaves 0.0055 (half of α) in the upper tail of the normal distribution.
Step-by-step explanation:
The student is looking for the critical value zα/2 that is used to construct a 98.9% confidence interval in statistics. The confidence level (CL) of 98.9% means the area in the central part of the standard normal distribution is 0.989 and the area in the tails (two tails combined) α is 1 - CL, which gives us 1 - 0.989 = 0.011. Hence, each tail will have an area of α/2, which is 0.011/2 = 0.0055.
To find the critical value, we look up the z-score that leaves 0.0055 in the upper tail of the normal distribution. From a z-table or using technology like a calculator, we can find that the z-score that corresponds to an upper tail of 0.0055 is approximately zα/2 = 2.576. Therefore, to construct a 98.9% confidence interval, we need to use the critical value zα/2 = 2.576.
This process of finding the critical value based on a desired confidence level is integral in hypothesis testing and interval estimation in statistics.