Question

An engineer wanted to estimate the true mean resistance of a certain electrical circuits (?) by a sample mean (?̅). It is known that the population is normal, and the population standard deviation is ? = 0.25 ohms. Determine the required sample size (?) so that he will be 90% confident of being correct within ± 0.06.

Answer 1

Solution:

Given:

The population standard deviation = = 0.25 ohms.

Confidence level = c = 90%

Margin of Error = E = 0.06

We have to find the required sample size (?):

Formula:

Z_c is z critical value for c = 90% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.90) / 2 = 1.90 / 2 = 0.9500

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_c = 1.645

thus

Thus  the required sample size (?) is 47