Answer to Question #155068 in Statistics and Probability for Ruth

Question

Question 1. Which is shorter, a 95% z-interval for the mean or a 95% t-interval for the mean? Is one of these always shorter, or does the outcome depend on the sample?

Answer 1

95 % confidence interval for mean is shorter for z-interval because t-critical is greater than z-critical value. Yes, z-interval is always shorter because t-critical value cannot be smaller than z-critical value.