Question

Construct the 99% confidence interval for the population mean duration of the longdistance calls from the town. 

Answer 1

Assumptions:

mean $\bar{x}= 12$

sample standard deviation s= 2

Sample size n = 100

alpha = 1%

The critical value for α=0.01 and df= n-1= 99 is $t_c = 2.626$

$CI = \bar{x} ± t_c \times \frac{s}{\sqrt{n}} \\ CI = 12 ± 2.626 \times \frac{2}{\sqrt{100}} \\ CI = (11.475, 12.525)$