Final answer:
To be 99% confident that an estimate of the average Florida rainfall is within 3 inches of the true average, with a known standard deviation of 9 inches, a z* critical value of 2.576 is required. The sample size needed is calculated to be 60 places in Florida after applying the appropriate formula and rounding up to the nearest whole number.
Step-by-step explanation:
When tasked with estimating the average Florida rainfall within a specific margin of error, one needs to determine the appropriate sample size. To answer the question, 'If you wanted to be 99% confident that your estimate of the average Florida rainfall was within 3 inches of the true average, how many places in Florida should you survey?' we need to use the z-distribution and the known standard deviation of 9 inches per year.
The z* critical value (i) associated with a 99% confidence level is approximately 2.576. This value can be found in statistical z-tables or using statistical software.
To calculate the required sample size (ii), use the formula for sample size in estimation:
where n is the sample size, z* is the z-score, σ (sigma) is the standard deviation, and E is the margin of error. Plugging the values into the formula:
- n = (2.576 × 9 / 3)^2
- n = (23.184 / 3)^2
- n = (7.728)^2
- n = 59.72
Since we can't survey a fraction of a place, we round up to the nearest whole number. Thus, you need to survey 60 places in Florida to be 99% confident that your estimate of the average Florida rainfall is within 3 inches of the true average.