Question

Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 397 elementary school teachers and 268 high school teachers. Of the elementary school teachers, 225 said they were very satisfied with their jobs, whereas 129 of the high school teachers were very satisfied with their work. Estimate the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied by calculating a 95% CI. (Use p_elementary − p_{high school}. Round your answers to four decimal places.)

( ), ( )

Answer 1

Solution:

Given:

Elementary school teachers:

n₁ = 397

x₁ = 225

and

High school teachers:

n₂ = 268

x₂ = 129

We have to estimate the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied by calculating a 95% CI.

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

95% confidence interval for  the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied is between ( 0.0082 , 0.1626 )