The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow

4 7 6 5 8 8 4 8 9  8 8 4 10 10 1 1 1 9 1 9 1 1 8 8 1 8 8 9 8 7 7 1 8 8 10 1 8 7 9 7 8 9 7 7 7 8 1 6 10 7

Develop a 95% confidence interval estimate of the population mean rating for Miami. round your answers to two decimal places


To develop a 95% confidence interval for the population mean, we can use the following formula:

\[
\text{Confidence Interval} = \bar{x} \pm z_{\alpha/2} \cdot \frac{s}{\sqrt{n}}
\]

Where:
- \(\bar{x}\) = sample mean
- \(s\) = sample standard deviation
- \(n\) = sample size
- \(z_{\alpha/2}\) = z-value corresponding to the 95% confidence level (for 95%, \(z_{\alpha/2} = 1.96\))

### Step 1: Calculate the sample mean (\(\bar{x}\))
The sample data provided is:
\[
4, 7, 6, 5, 8, 8, 4, 8, 9, 8, 8, 4, 10, 10, 1, 1, 1, 9, 1, 9, 1, 1, 8, 8, 1, 8, 8, 9, 8, 7, 7, 1, 8, 8, 10, 1, 8, 7, 9, 7, 8, 9, 7, 7, 7, 8, 1, 6, 10, 7
\]

The sample size \(n = 50\).

Let's calculate the sample mean \(\bar{x}\) and the standard deviation \(s\):

\[
\bar{x} = \frac{\text{sum of the sample data}}{n}
\]

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

### Step 2: Find the z-value for a 95% confidence level
For a 95% confidence interval, the \(z_{\alpha/2}\) value is 1.96.

### Step 3: Calculate the confidence interval

Using the formula:

\[
\text{Confidence Interval} = \bar{x} \pm 1.96 \cdot \frac{s}{\sqrt{50}}
\]

Let me compute the results for you.

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow: 4, 7, 6, 5, 8, 8, 4, 8, 9, 8, 8, 4, 10, 10, 1, 1, 1, 9, 1, 9, 1, 1, 8, 8, 1, 8, 8, 9, 8, 7, 7, 1, 8, 8, 10, 1, 8, 7, 9, 7, 8, 9, 7, 7, 7, 8, 1, 6, 10, 7. Develop a 95% confidence interval estimate of the population mean rating for Miami. Round your answers to two decimal places.

Calculate the 95% confidence interval for the population mean rating of Miami International Airport based on a sample of 50 business travelers. Learn about key statistical concepts such as confidence intervals, sample mean, and standard deviation.

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