Question

Use the given margin of​ error, confidence​ level, and population standard​ deviation, sigma​, to find the minimum sample size required to estimate an unknown population​ mean, mu. Margin of​ error: 1.1 ​inches, confidence​ level: 90​%, sigmaequals2.9 inches A confidence level of 90​% requires a mimimum sample size of ______. ​(Round up to the nearest​ integer.)

Answer 1

19

Explanation:

Margin of Error (E) = t × sd/√n

√n = t ×sd/E

n = (t × sd/E)^2

Using a 90% confidence level, t = 1.645, sd = 2.9 inches, E = 1.1 inches

n = (1.645 × 2.9/1.1)^2 = 4.34^2 = 18.807

Minimum sample size required = 19 (to the nearest integer)