Question

A random sample of 117 full-grown lobsters had a mean weight of 23 ounces. Assume that the population standard deviation = 3.4 ; Construct a 95% confidence interval for the population mean.

Options:

* A - 22.5 to 23.5 ounces

* B - 22.2 to 23.8 ounces

* C - 22.4 to 23.6 ounces

* D - 22.3 to 23.7 ounces

Answer 1

Solution:

Given:

Sample size = n = 117

Sample mean =

The population standard deviation =

We have to construct a 95% confidence interval for the population mean.

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 correct answer is: C - 22.4 to 23.6 ounces