In December 2004, a report based on the National Survey on Drug Use and Health estimated that 20% of all Americans of ages 16 to 20 drove under the influence of drugs or alcohol in the previous year (AP, December 30, 2004). A public health unit in Wellington, New Zealand, plans a similar survey for young people of that age in New Zealand. They want a 95% confidence interval to have a margin of error of 0.04.
a. Find the necessary sample size if they expect results similar to those in the United States.
b. Suppose that in determining the sample size, they use the safe approach that sets p̂ = 0.50 in the formula for n. Then, how many records need to be sampled? Compare this to the answer in part a. Explain why it is better to make an educated guess about what to expect for p̂, when possible.