Question

A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with 95​% confidence if ​

(a) she uses a previous estimate of 0.36? (round up to the nearest integer) ​(b) she does not use any prior​ estimates? (round up to the nearest integer)

Answer 1

Solution:

Given:

E = Margin of Error = 0.03

c = confidence level = 0.95

We have to find sample size n to estimate the proportion of adults who have​ high-speed Internet access.

Part a) If she uses a previous estimate of 0.36.

that is: p= 0.36

Formula:

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

( Sample size is always rounded up)

Part b) If she does not use any prior​ estimates.

Then we use p =0.5

thus