Suppose that, based on a simple random sample of n = 100 American adult men, we wish to calculate a 98% confidence interval for the population mean height µ. For this confidence interval, the critical values ± z* could be calculated from:
the 1st percentile of a N(0, 1) distribution.
the 2nd percentile of a N(0, 1) distribution.
the 2.5th percentile of a N(0, 1) distribution.
the 98th percentile of a N(0, 1) distribution.
The critical values ± z* could be calculated from the 2.5th percentile of a N(0, 1) distribution.
In a 98% confidence interval, we want to capture 98% of the area under the normal distribution curve, which leaves 2% in the two tails. Therefore, we need to find the value of z* that corresponds to the 2.5th percentile of the standard normal distribution for each tail.
By symmetry, we divide the 2% into two tails, so each tail has an area of 1%. To find the z-score corresponding to the 1% tail, we look for the value in the standard normal distribution table that gives us a cumulative probability of 0.01. This value is z*.
So, the critical values ± z* could be calculated from the 2.5th percentile of a N(0, 1) distribution.