Question

The standard deviation for the weights of newborn elephants is known to be 20 pounds. We want to construct a 95% confidence interval for the mean weight of newborn baby elephants. Forty newborn baby elephants are weighed with a sample mean of 264 pounds and a sample standard deviation of 16 pounds. Find the confidence interval. Round your answer to the nearest hundredth.

Answer 1

Solution:
Given:

The standard deviation for the weights of newborn elephants is known to be 20 pounds.

that is: pounds

Sample size = n = 40

Sample mean =   pounds

We have to construct a 95% confidence interval for the mean weight of newborn baby elephants.

Formula:

where

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

Thus we are   95% confident that the mean weight of newborn baby elephants is between 257.80 pounds to 270.20 pounds.