To calculate the 95% confidence interval (CI) for the true proportion of exoplanets that exist in multiple-star systems, we will use the following formula for a confidence interval for a population proportion:

$\text{CI} = \hat{p} \pm Z_{\alpha/2} \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

Where:

• $\hat{p}$ is the sample proportion.
• $Z_{\alpha/2}$ is the z-score corresponding to the desired confidence level.
• $n$ is the sample size.

Step 1: Calculate the sample proportion $\hat{p}$

$\hat{p} = \frac{17}{38}$

Step 2: Determine the z-score for a 95% confidence level

For a 95% confidence interval, the z-score ($Z_{\alpha/2}$) is 1.96.

Step 3: Plug the values into the formula and calculate the confidence interval

Let's compute the values.The 95% confidence interval for the true proportion of multi-star exoplanets among all detected exoplanets is:

• Lower bound (smaller number): 0.289
• Upper bound (bigger number): 0.605

Would you like further details or have any questions?

Here are 5 related questions to consider:

1. What factors could influence the proportion of exoplanets found in multi-star systems?
2. How would the confidence interval change with a larger sample size?
3. What is the interpretation of this confidence interval in the context of exoplanet research?
4. How does the z-score affect the width of the confidence interval?
5. What are some other statistical methods used in analyzing exoplanet data?

Tip: Increasing the sample size reduces the margin of error, leading to a narrower confidence interval.