Final answer:
To report a 97% confidence interval for the average Florida rainfall, the necessary statistical information is the sample mean, sample standard deviation, and the sample size. These elements are used to estimate the margin of error and construct the confidence interval that is expected to contain the true population mean 97% of the time.
Step-by-step explanation:
To report an appropriate 97% one-sample confidence interval for the average Florida rainfall, you need to have the sample mean and the sample standard deviation. These statistics are essential because the confidence interval is an estimate of an unknown population parameter, which is likely to include the true average rainfall within a certain range. For a 97% confidence interval, the desired confidence level essentially means that if we were to take multiple samples and create confidence intervals from these samples, 97% of those intervals would contain the true population mean.
The sample size is also critical as it impacts the margin of error of the confidence interval. A larger sample size typically results in a smaller margin of error, making the confidence interval narrower. Therefore, both the sample size and the sample standard deviation are needed to calculate the margin of error and, ultimately, the confidence interval.
When computing a confidence interval, we assume that the sample mean, denoted as x, is a point estimate for the population mean, μ, and that the sample standard deviation, denoted as s, is a point estimate for the population standard deviation, σ. In summary, the necessary statistical information includes the mean and standard deviation of the sample, alongside the sample size, to estimate a 97% confidence interval for Florida rainfall.