Final answer:
To create a 95% confidence interval estimate for Miami's population mean rating in Excel, find the sample mean and margin of error, then apply the formula: sample mean ± margin of error. A 95% confidence interval implies we are 95% confident the true mean falls within this interval, which will be wider compared to a 90% confidence interval to increase the likelihood of containing the true mean.
Step-by-step explanation:
To develop a 95% confidence interval estimate of the population mean rating for Miami using Excel, we want to identify the sample mean (μ), calculate the margin of error, and apply the formula: sample mean ± margin of error. The margin of error is typically computed by taking the standard error (which is the standard deviation of the sample divided by the square root of the sample size) and multiplying it by the critical value from the t-distribution or z-distribution that corresponds to our 95% confidence level.
A 95% confidence interval means that if we were to take many samples and create confidence intervals for each, we would expect that approximately 95% of these intervals would contain the true population mean. Therefore, when we say that the interval is (4.5, 9.5), we estimate with 95% confidence that the true population mean lies within this range.
Comparing the 90% confidence interval with the 95% confidence interval, we note that the latter is wider because a higher level of confidence requires a larger range to ensure that the true mean is likely to be captured within the interval.