Final answer:
To be 95% confident with a margin of error of no more than three percentage points, the programmer should survey at least 1,068 computers.
Step-by-step explanation:
Survey Sample Size Calculation
To determine the number of computers that must be surveyed to estimate the percentage of computers that use a new operating system with 95% confidence and an error margin of no more than three percentage points, the following formula for sample size (n) can be used:
n = (Z^2 * p * (1 - p)) / E^2
Where:
- Z is the Z-score for the desired confidence level
- p is the estimated proportion of the population
- E is the margin of error
If nothing is known about the percentage of computers with new operating systems, a conservative approach is to use p = 0.5, as this maximizes the product p*(1-p) and thus the sample size. For a 95% confidence level, the Z-score is commonly 1.96. Substituting these values into the formula:
n = (1.96^2 * 0.5 * (1 - 0.5)) / 0.03^2
n = (3.8416 * 0.25) / 0.0009
n = 1,067.11
Therefore, the programmer should survey at least 1,068 computers (rounded up to the nearest integer) to meet the requirements.