Question

Confidence Interval. Calculate a 80% confidence interval to estimate the population mean using the following data: Sample mean = 20, sample standard deviation =5, sample size = 16. Do not forget conclusion.

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

n = 16

df = n – 1 = 15

Confidence level = 80%

Critical t value = 1.3406

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 20 ± 1.3406*5/sqrt(16)

Confidence interval = 20 ± 1.6758

Lower limit = 20 - 1.6758 = 18.324

Upper limit = 20 + 1.6758 = 21.676

Confidence interval = (18.324, 21.676)

We are 80% confident that the population mean will lies between 18.324 and 21.676.