Question

New York Times article reported that a survey conducted in 2014 included 40000 adults, with 4.1% 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 99.5% and a margin of error of 2 percentage are wanted?

a) Assume that nothing is known about the rate of e-cigarette usage among aduits. The sample size is Use the results from the 2014 survey. The sample size is Note: You can earn partial credit on this problem.

Answer 1

To estimate today's usage rate of e-cigarettes among adults, you would need to survey approximately 1917 adults.

Step-by-step explanation:

To determine the sample size needed to estimate today's usage rate of e-cigarettes among adults, we can use the formula for sample size calculation for proportions:

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

Where:

• n is the required sample size
• Z is the z-value corresponding to the desired confidence level (99.5% is approximately 2.807)
• p is the estimated proportion of e-cigarette users based on the 2014 survey (4.1% = 0.041)
• E is the desired margin of error (2 percentage points = 0.02)

Plugging in these values, we get:

n = (2.807^2 * 0.041 * (1 - 0.041)) / 0.02^2

Solving for n:

n = 1916.563

Rounding up to the next higher value, the sample size needed is 1917 adults.