Question

In December 2004, a report based on the National Survey on Drug Use and Health estimated that 20% of all Americans aged 16 to 20 drove under the influence of drugs or alcohol in the previous year. We would like to update this information by calculating a 98% confidence interval. How large a sample is necessary in order for the bound on the error of estimation to be 0.04?

Answer 1

542

Explanation:

We are required to find the sample size at 98% confidence interval in this question

E = 0.04

P* = 20% = 0.20

n = p* x (1-p)(Zα/2÷E)²

α = 1 - 0.98

= 0.02

To get Critical value

= 0.02/2 = 0.01

The critical value at 0.01 is 2.33

Inserting values into formula:

O.2 x 0.8(2.33/0.04)²

= 0.8 x 0.2 x 58.25²

= 542.89

The value of n must be an integer therefore the answer is 542.