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The problem is asking to calculate the 95% confidence interval for the average expenditure of a sample of household heads on clothing, given the data of their expenditures (in hundred thousands of rupiahs).

The steps to calculate the confidence interval for the mean are as follows:

1. **Calculate the sample mean (\( \bar{x} \)):**
   \[
   \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}
   \]
   where \( n \) is the number of samples and \( x_i \) are the sample values.

2. **Calculate the sample standard deviation (\( s \)):**
   \[
   s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}}
   \]
   
3. **Calculate the standard error (SE):**
   \[
   SE = \frac{s}{\sqrt{n}}
   \]

4. **Determine the critical value (t*) for a 95% confidence level:**
   Since the sample size is small (\( n = 20 \)), we use the t-distribution with \( n-1 = 19 \) degrees of freedom.

5. **Compute the confidence interval (CI):**
   \[
   CI = \bar{x} \pm (t^* \cdot SE)
   \]

Let me calculate the values for you using the data provided.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you through the calculations step by step if you prefer to do them manually:

1. **Calculate the mean** of the provided data set.
2. Find the **sample standard deviation**.
3. Calculate the **standard error**.
4. Look up the **t-critical value** for a 95% confidence interval with 19 degrees of freedom.
5. Compute the confidence interval using the formula provided earlier.

Let me know if you'd like help with any of these steps! Here are some related questions:

1. How is the t-distribution used for small sample sizes?
2. What factors influence the width of a confidence interval?
3. How does the standard deviation impact the confidence interval?
4. How can you find the critical t-value for different confidence levels?
5. What are the differences between using the z-distribution and the t-distribution?

**Tip**: Always ensure your sample size is representative of the population to minimize error in your estimates.

Hitunglah confidence interval 95% rata-rata pengeluaran kepala keluarga tersebut.

Learn how to calculate the 95% confidence interval for the average household expenditure on clothing. The sample data is based on 20 family heads and includes statistical concepts such as the sample mean, standard deviation, and the t-distribution.

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