To develop a 95% confidence interval for the population mean rating, we’ll follow these steps:

1. Calculate the sample mean ($\bar{x}$).
2. Calculate the sample standard deviation ($s$).
3. Determine the standard error of the mean.
4. Use the t-distribution to find the confidence interval.

Let's go through each calculation:

Step 1: Calculate the Sample Mean ($\bar{x}$)

The sample mean $\bar{x}$ is calculated as:

$\bar{x} = \frac{\sum x_i}{n}$

Where $x_i$ represents each rating, and $n = 50$.

Step 2: Calculate the Sample Standard Deviation ($s$)

The sample standard deviation $s$ is calculated using:

$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}$

Step 3: Calculate the Standard Error of the Mean (SEM)

The standard error of the mean is calculated by:

$\text{SEM} = \frac{s}{\sqrt{n}}$

Step 4: Find the t-value and Confidence Interval

Since the sample size is 50, we use the t-distribution with $n-1 = 49$ degrees of freedom. For a 95% confidence level, the two-tailed t-value (from a t-table) is approximately 2.0096.

The confidence interval is then:

$\bar{x} \pm (t \times \text{SEM})$

I'll proceed with the calculations to provide the exact values.The sample mean rating for Miami International Airport is $6.34$. Based on a 95% confidence level, the confidence interval for the population mean rating is approximately:

$(5.73, 6.95)$

This interval suggests that we can be 95% confident that the true mean rating for Miami International Airport lies between 5.73 and 6.95.

Would you like further details or have any questions?

Here are some follow-up questions to explore:

1. What would the confidence interval be if we wanted a 99% confidence level?
2. How would a larger sample size affect the width of the confidence interval?
3. What assumptions are made in this analysis about the ratings?
4. Can we use the normal distribution instead of the t-distribution in this case?
5. How would an outlier affect the sample mean and standard deviation?

Tip: Confidence intervals provide a range within which we expect the population parameter to fall, based on our sample data, helping in making informed estimates.