Answer:
A sample of 2017 should be taken.
Explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.

In which
z is the zscore that has a pvalue of
.
The margin of error is of:

Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of 0.30.
This means that

Confidence level:
Not given, so I will use 95%.
This means that
, z is the value of Z that has a pvalue of
, so
.
a. [2.5 pts] How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of 0.02?
A sample of n should be taken.
n is found fo M = 0.02. So






Rounding up:
A sample of 2017 should be taken.