Final answer:
A 95% confidence interval implies a 5% chance that the true parameter is not within the interval, hence a 5% Type I error rate when testing the null hypothesis that a parameter equals a specified value, due to the direct relationship between confidence intervals and Type I error rates.
Step-by-step explanation:
Achieving a 95% confidence interval coverage rate for a parameter (θ) implies that there is a 5% chance that the true population parameter is not contained within the interval. When testing the hypothesis H0: θ = θ0, rejecting the null hypothesis when it is indeed true constitutes a Type I error. The coverage rate of the confidence interval and the Type I error rate are directly related; with a 95% confidence interval, we are accepting a 5% Type I error rate. This is because the confidence interval is constructed to contain the true parameter 95% of the time, meaning there is a 5% chance that any given confidence interval does not contain the true parameter – hence, the same 5% chance of incorrectly rejecting the null hypothesis when it is true if the true parameter lies outside the specified confidence interval.
For a two-sided 95% confidence interval, there is 2.5% of the probability in each tail of the normal distribution. This signifies that there is a 2.5% chance the true parameter is lower than the lower bound and a 2.5% chance it is higher than the upper bound – totaling up to a 5% Type I error rate.