A Single Population Mean using the Normal Distribution · Example 4

Leave everything the same except the sample size. Use the original 90% confidence level. What happens to the error bound and the confidence interval if we increase the sample size and use n = 100 instead of n = 36? What happens if we decrease the sample size to n = 25 instead of n = 36?

• $\bar{x}$ = 68
• EBM = $\left(z_{\frac{\alpha }{2}}\right)\left(\frac{\sigma }{\sqrt{n}}\right)$
• σ = 3; The confidence level is 90% (CL=0.90); $z_{\frac{\alpha }{2}}$ = z_0.05 = 1.645.

OpenStax, Introductory Statistics 2e · §8.1 A Single Population Mean using the Normal Distribution · Example 4