Answer:
To calculate the minimum sample size required for a given margin of error and confidence level, we can use the following formula:
n = (z^2 * p * (1-p)) / E^2
where:
- n is the sample size
- z is the z-score for the desired confidence level (in this case, 99%, which corresponds to a z-score of 2.576)
- p is the estimated proportion of the population that has the characteristic of interest (since we don't have an estimate for p, we can use 0.5, which will give us the largest possible sample size)
- E is the desired margin of error (in this case, 0.05)
Substituting the values, we get:
n = (2.576^2 * 0.5 * (1-0.5)) / 0.05^2
n = 664.3
Rounding up to the nearest whole number, the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at a 99% confidence level is 665.