Question

Assume that a sample is used to estimate a population mean μ. Find the 95% confidence interval for a sample of size 1037 with a mean of 38.4 and a standard deviation of 19.2. Enter your answer as a tri-linear inequality accurate to 3 decimal places.
_______< μ < _______

Answer 1

Solution:

Given:

n= sample size = 1037

Sample mean =

Sample standard deviation = s = 19.2

Find 95% confidence interval:

where

Since population standard deviation is unknown we use sample standard deviation s and since sample size n is large, we use z.

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

thus

Thus