Final answer:
The critical t-value tα/2 for constructing a 98% confidence interval from a sample size of n = 22 can be obtained using a t-distribution table or calculator, with degrees of freedom equal to 21.
Step-by-step explanation:
To find the critical value tα/2 needed to construct a 98% confidence interval for a sample size of n = 22, with the population following a normal distribution, we must consult a t-distribution table or use a statistical calculator program that can provide this value. A t-distribution is appropriate here due to the sample size being less than 30 and the population standard deviation being unknown.
For a 98% confidence interval, the total area in the tails is 2% (since confidence level + tail areas = 100%). The area in each tail is 1%, or 0.01. Hence, we seek tα/2 such that the area in the upper tail is 0.01. As the sample size is 22, the degrees of freedom (df) would be df = n - 1 = 22 - 1 = 21.
With these parameters, we would use either a table or a calculator to find the value of t such that 1% of the area of the t-distribution is to the right of this value, which would provide us with the desired critical value tα/2.