Final answer:
To reduce the margin of error in a poll from 4% to a lower value, the sample size needs to be increased. The margin of error is inversely proportional to the square root of the sample size, so by surveying more individuals, the precision of the poll results can be improved.
Step-by-step explanation:
To reduce the margin of error in a poll where only 100 people were surveyed, and presently there is a margin of error of 4%, a larger sample size needs to be surveyed. The margin of error is inversely proportional to the square root of the sample size; consequently, increasing the sample size will decrease the margin of error. To calculate the required sample size to achieve a lower margin of error, we can use the formula for the margin of error in proportion polls at a 95% confidence level: ME = Z * sqrt((p*(1-p))/n), where ME is the desired margin of error, Z is the Z-score (1.96 for 95% confidence), p is the proportion (expressed as a decimal), and n is the sample size.
Given the desire for a lower margin of error, let us say we want to achieve a margin of error of 3% instead of 4%. We would then solve the above formula for n to find the new required sample size. It is also important to note that while increasing the sample size can reduce the margin of error, practical considerations such as time and cost constraints must be taken into account when deciding on the final sample size for a survey.