A New York Times article reported that a survey conducted in 2014 included 36,000 adults, with $3.68 \%$ 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 $95 \%$ and a margin of error of 1.5 percentage points are wanted? Complete parts (a) through (c) below.
a. Assume that nothing is known about the rate of e-cigarette usage among adults.
\[
n=4269
\]
(Round up to the nearest integer.)
b. Use the results from the 2014 survey.
\[
\mathrm{n}=606
\]
(Round up to the nearest integer.)
c. Does the use of the result from the 2 cily survey have much of an effect on the sample size?
A. No, using the result from the 2014 survey only slightly reduces the sample size.
B. Yes, using the result from the 2014 survey only slightly increases the sample size.
C. No, using the result from the 2014 survey does not change the sample size.
D. Yes, using the result from the 2014 survey dramatically reduces the sample size.

Step 1 ：Given that the confidence level is 95%, the corresponding z-score is approximately 1.96. The desired margin of error is 1.5 percentage points, or 0.015.

Step 2 ：For part a, we don't know the proportion of e-cigarette users, so we'll use the worst-case scenario, which is p = 0.5. This maximizes the product p*(1-p). We can then use the formula for calculating the sample size for a proportion: \(n = \frac{Z^2 * p * (1-p)}{E^2}\). Substituting the given values, we find that the required sample size is \(n = \frac{(1.96)^2 * 0.5 * (1-0.5)}{(0.015)^2}\), which rounds up to 4269.

Step 3 ：For part b, we'll use the proportion from the 2014 survey, which is 0.0368. Substituting this value into the formula, we find that the required sample size is \(n = \frac{(1.96)^2 * 0.0368 * (1-0.0368)}{(0.015)^2}\), which rounds up to 606.

Step 4 ：For part c, we compare the sample sizes calculated in parts a and b. We see that using the result from the 2014 survey dramatically reduces the sample size.

Step 5 ：Final Answer: For part a, the required sample size is \(\boxed{4269}\). For part b, the required sample size is \(\boxed{606}\). For part c, the answer is \(\boxed{\text{D. Yes, using the result from the 2014 survey dramatically reduces the sample size.}}\)