Answer to Question #228965 in Statistics and Probability for Millicent

Question

If sample mean = 54, sample standard deviation = 6, sample size = 25, confidence level = 90%, calculate the confidence interval for the estimate of the population mean.

Select one:

a. 51.95; 56.05

b. 54.8; 90.1

c. 50.6; 54.5

d. 6.0; 25.2

Answer 1

$M = 54 \\ \sigma = 6 \\ n=25$

Two-sided confidence interval:

$CI = (M - \frac{Z_c \times \sigma}{\sqrt{n}}, M + \frac{Z_c \times \sigma}{\sqrt{n}})$

For 90 % confidence level

$Z_c=1.645 \\ CI = (54 - \frac{1.645 \times 6}{\sqrt{25}}, 54 + \frac{1.645 \times 6}{\sqrt{25}}) \\ =(54-1.974, 54+1.974) \\ = (52.026, 55.974)$

There is no right option.