Question

You measure 52 textbooks' weights, and find they have a mean weight of 65 ounces. Assume the population standard deviation is 7.8 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.

Give your answers as decimals, to two places

? < μ < ?

Answer 1

Solution:

Given:

Sample size = Number of textbooks' = 52

Sample mean = ounces.

Population standard deviation =   ounces.

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

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