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The problem asks to calculate a 90% confidence interval for the mean daily return of a stock, based on a random sample of 10 days.

To do this, we will follow these steps:

### 1. Calculate the sample mean (\(\bar{x}\)):
The data provided is:
\[
2.04, 1.99, 0.99, 2.32, 1.74, -1.79, -2.18, 2.69, 1.9, -1.76
\]

We will calculate the mean of these values.

### 2. Calculate the sample standard deviation (\(s\)):
We will also calculate the standard deviation for this sample of 10 values.

### 3. Use the t-distribution:
Since the sample size is less than 30, we will use the t-distribution to find the confidence interval. For a 90% confidence level and 9 degrees of freedom (\(n-1 = 10 - 1 = 9\)), the critical value \(t_{\alpha/2}\) can be obtained from t-tables or a calculator.

### 4. Confidence interval formula:
The formula for the confidence interval is:
\[
\bar{x} \pm t_{\alpha/2} \left(\frac{s}{\sqrt{n}}\right)
\]

Let me now compute the values.The calculations are as follows:

- Sample mean (\(\bar{x}\)) = 0.794 (rounded to three decimal places)
- Sample standard deviation (\(s\)) = 1.918
- Lower limit of the 90% confidence interval = -0.318
- Upper limit of the 90% confidence interval = 1.906

Therefore, the 90% confidence interval for the mean daily return is approximately \((-0.3, 1.9)\).

Would you like more details or have any questions?

Here are some related questions:
1. What happens to the confidence interval if we increase the confidence level to 95%?
2. How does the sample size affect the width of the confidence interval?
3. Why do we use the t-distribution instead of the normal distribution in this case?
4. Can we say that the true mean return will always lie within this confidence interval?
5. What are some assumptions behind using confidence intervals?

**Tip:** The confidence interval provides a range of values within which we expect the true population mean to lie with a specified probability (e.g., 90%).

A certain brokerage house wants to estimate the mean daily return on a certain stock. A random sample of 10 days yields the following return percentages: 2.04, 1.99, 0.99, 2.32, 1.74, -1.79, -2.18, 2.69, 1.9, -1.76. Find the 90% confidence interval for the mean daily return.

Learn how to calculate a 90% confidence interval for the mean daily return of a stock based on a random sample of 10 days. This example involves key statistical concepts such as sample mean, standard deviation, and the t-distribution. Find out the lower and upper limits of the confidence interval.

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