Question

The lengths of text messages are normally distributed with a population standard deviation of 6 characters and an unknown population mean. If a random sample of 27 text messages is taken and results in a sample mean of 25 characters, find a 95% confidence interval for the population mean. Round your answers to two decimal places. z0.10 z0.05 z0.04 z0.025 z0.01 z0.005 1.282 1.645 1.751 1.960 2.326 2.576 You may use a calculator or the common z-values above.

Answer 1

(22.74 ; 27.26)

Explanation:

The confidence interval relation is stated as :

Mean ± Zcritical * σ/sqrt(n)

Mean = 25

σ = 6

The Zcritical at 95% = 1.96

Hence,

25 ± 1.96 * (6/sqrt(27))

25 ± 1.96 * 1.1547005

Lower boundary :

25 - (1.96 * 1.1547005) = 22.73678702

Upper boundary :

25 + (1.96 * 1.1547005) = 27.26321298

(22.74 ; 27.26)