Final answer:
When asked to find the 95% confidence interval of the mean, α for each tail of the distribution is 0.025 or 2.5%. This is because a 95% confidence interval covers the central 95% of the probability, leaving 5% to be split equally between the two tails.
Step-by-step explanation:
When constructing a two-sided 95% confidence interval for the mean, the value of α (alpha) for each tail of the distribution is calculated based on the remaining percentage not covered by the confidence interval. Since a 95% confidence interval covers 95% of the probability within the center of the distribution, the remaining 5% is not included. This 5% is equally divided between the two tails of the normal distribution. Therefore, each tail will have an α of 0.025 or 2.5%. This means that there is a 2.5% chance that a sample mean will fall into either the lower or upper tail of the distribution, assuming the null hypothesis is true.
To find the value for z that corresponds to this α, you would look up the z-score that has an area of 0.025 to its right, which is approximately 1.96. Thus, when calculating the 95% confidence interval, statisticians often use z₀€₀₂₅ = ±1.96 to determine the range around the sample mean.