A researcher wishes to estimate, with 95% confidence, the proportion who own a laptop. A previous study shows that 70% of those interviewed had a laptop computer. How large a sample should the researcher select so that the estimate will be within 3% of the true proportion?

The sample needs to be at least n = 897 in size.

Step-by-step explanation:

Given

Confidence Level = 95%

Let p = those who had laptop

p = 70% = 0.7

Margin of Error = 3% = 0.03

Let n = required sample.

To estimate the proportion of laptop owners with 95% confidence, first the z-value is calculated.

Given that confidence level = 95%

α  =  1 − 95 %

α  =  1 − 0.95  

α =  0.05  

So;

=

=

From the z table

Using formula for margin of error

where p + q =1

q = 1 - p

q = 1 - 0.7

q = 0.3

So,

--- Make n the subject of formula

First, square both sides

------ Multiply both sides by

Hence, the sample needs to be at least n = 897 in size.