Question

. A sample of 25 items yields X(bar) = 60 grams and s = 9 grams. Assuming a normal parent distribution, construct a 99 percent confidence interval for the population mean weight.

Answer 1

Given, = 60, s = 9, n = 25

Since population standard deviation is unknown and n < 30, we use the t distribution

The tcritical (2 tail) for = 0.01, degrees of freedom = n - 1 = 25 - 1 = 24 is 1.960

The Confidence Interval is given by ME, where

The Lower Limit = 60 - 5.035 = 54.965

The Upper Limit = 60 + 5.035 = 65.035

The 99% Confidence Interval is 54.965 , 65.035