Question

The sampled population is normally distributed, with the given information. (Give your answers correct to two decimal places.)

n = 11, x = 29.6, and σ = 6.4

(a) Find the 0.99 confidence interval for μ.
to  

Answer 1

Solution:

Given: n = 11,   , and σ = 6.4. The sampled population is normally distributed

We have to find a 99% confidence interval for μ.

Formula:

where

Where Z_c is z critical value for c = 0.99 confidence level.

Find Area = ( 1+c)/2 = ( 1 + 0.99 ) / 2 = 1.99 /2 = 0.9950

Thus look in z table for Area = 0.9950 or its closest area and find corresponding z critical value.

From above table we can see area 0.9950 is in between 0.9949 and 0.9951 and both are at same distance from 0.9950, Hence corresponding z values are 2.57 and 2.58

Thus average of both z values is 2.575

Thus Z_c = 2.575

Thus

Thus

Thus a 99% confidence interval for μ is from 24.63 to 34.57