Question

construct the indicated confidence interval for the population mean using the t distribution. Assume the population js normally distributed. c=0.99, x=12.1,s=0.76,n=17

Answer 1

Solution:

Given:

Sample size = n = 17

Sample mean =

Sample standard deviation = s = 0.76

Confidence level = c = 99% = 0.99

Formula:

where

tc is t critical value for c = 99%  confidence level

Thus two tail area = 1 - c = 1 - 0.99 = 0.01

df = n - 1 =  17 - 1 = 16

Look in  t table for df = 16 and two tail area = 0.01 and find t critical value

t_c = 2.921

thus

thus

thus a 99% confidence interval for population mean is between 11.56 and 12.64