Question

A sample of 40 CDs from a student's collection showed a mean length of 52.74 minutes with a standard deviation of 13.21 minutes. Construct a 95% confidence interval for the population standard deviation. (Round your answers to 4 decimal places.) The 95% confidence interval is from to .

Answer 1

(48.65, 56.83)

Explanation:

Given that :

Sample size (n) = 40

Mean (m) = 52.74

Standard deviation (s) = 13.21

α = 95%

Confidence interval around sample mean can be obtained using the relation :

Mean ± Zstatistic * s/√n

Z score for 95% confidence interval = 1.96 (Z probability calculator)

s / √n = 13.21 / √40 = 2.0886843

Lower limit of confidence interval :

52.74 - (1.96 * 2.0886843) = 48.646178772 = 48.65

Upper limit of confidence interval :

52.74 + (1.96 * 2.0886843) = 56.833821228 = 56.83