Single-sample, Large Sample Confidence Interval for a Mean
Sometimes you are confronted with a deceptively simple-looking problem:
Construct the indicated confidence interval for the population mean, µ.
c = 0.90, x-bar = 16.2, s = 5.0, n = 75.
To solve it you need to carefully inspect the data you are given. You should notice two things. You are not given the population standard deviation, σ, and the n is > 30.
Depending upon the author of your stats book (and your instructor), you will choose either the normal distribution or the t-distribution to solve it. Some authors (e.g. Larson) say if you do not know sigma, use the t-distribution. Other authors say if n > 30, it is OK to use the normal distribution with s being approximately equal to σ. (McClave, Benson, & Sincich, 2014, p 303)