Question

Consider a population with a known standard deviation of 26.8. In order to compute an interval estimate for the population mean, a sample of 64 observations is drawn. Compute the margin of error for a 99% confidence level. Round your answer to 2 decimal places.

Answer 1

Solution:

Given:

Population standard deviation =

Sample size = n = 64

Confidence level = c = 99%

We have to find the margin of error for a 99% confidence level.

Formula:

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 the margin of error for a 99% confidence level is E = 8.63