Question

A New York Times article reported that a survey conducted in 2014 included 36000 ​adults, with ​3.66% of them being regular users of​ e-cigarettes. Because​ e-cigarette use is relatively​ new, there is a need to obtain​ today's usage rate. How many adults must be surveyed now if a confidence level of ​90% and a margin of error of 1 percentage point are​ wanted? Use the results from the 2014 survey to find n

Answer 1

To determine the sample size needed to obtain today's usage rate of e-cigarettes with a confidence level of 90% and a margin of error of 1 percentage point, approximately 1358 adults must be surveyed.

Step-by-step explanation:

To determine the sample size needed to obtain today's usage rate of e-cigarettes with a confidence level of 90% and a margin of error of 1 percentage point, we can use the formula for sample size calculations:

n = (Z^2 * p * (1-p)) / E^2

Where:

• n is the sample size
• Z is the z-score corresponding to the desired confidence level
• p is the estimated proportion of e-cigarette users based on the 2014 survey
• E is the margin of error (expressed as a proportion)

Using the information given, we can substitute the values into the formula:

n = (1.645^2 * 0.0366 * (1-0.0366)) / 0.01^2

n ≈ 1358

Therefore, approximately 1358 adults must be surveyed now to obtain today's usage rate of e-cigarettes with a confidence level of 90% and a margin of error of 1 percentage point.

Learn more about Sample size calculation here: