Question

A child psychologist wishes to estimate the percentage of fathers who watch their preschool-aged child when the mother works. What size sample should be obtained if she whises the estimate to be within 3 percentage points with 97% confidence if

A. she uses a 2005 estimate of 82% obtained from the U.S Census Bureau?

Z= n=

B. She does not use any prior estimates.

n=

Answer 1

Solution:

Given:

p = proportion of fathers who watch their preschool-aged child when the mother works

E = Margin of Error = 3% = 0.03

c = Confidence level = 97%

Part A) Find sample size when p = 82% = 0.82

Formula:

We need to find z_c value for c=97% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.97) /2 = 1.97 / 2 = 0.9850

Area 0.9850 corresponds to 2.1 and 0.07

Thus z = 2.17

that is: z_c = 2.17

Thus we get :

( Note: Sample size is always rounded up)

Part B) She does not use any prior estimates.

Thus we use p = 0.5

Thus we get: