Final answer:
To estimate the percentage of adults who support abolishing the penny with 90% confidence and a margin of error of 4 percentage points, a sample size of 683 is required.
Step-by-step explanation:
To determine the sample size required to estimate the percentage of adults who support abolishing the penny with 90% confidence and a margin of error of 4 percentage points, we can use the formula:
n = (Z^2 * p * (1-p)) / (E^2)
Where:
- n is the required sample size
- Z is the Z-score corresponding to the desired confidence level
- p is the estimated proportion
- E is the margin of error
Given that the previous estimate of the proportion is 25%, and the desired confidence level is 90%, we can substitute these values into the formula:
Z = 1.645 (for 90% confidence level)
p = 0.25
E = 0.04
Substituting these values, we get:
n = (1.645^2 * 0.25 * (1-0.25)) / (0.04^2)
Simplifying the equation:
n = 682.129
Rounding up to the nearest whole number, the researcher should obtain a sample size of 683 in order to estimate the percentage of adults who support abolishing the penny within 4 percentage points with 90% confidence.