A certain brokerage house wants to estimate the mean daily return on a certain stock. A random sample of 15 days yields the following return percentages.

-2.57, -0.74, 2.38, -0.76, -2.79, 2.05, -1.11, 1.83, -1.6, 2.31, 0.44, 2.66, -1.81, 0.91, -1.5


If we assume that the returns are normally distributed, find a 90% confidence interval for the mean daily return on this stock. Give the lower limit and upper limit of the 90% confidence interval.

Carry your intermediate computations to at least three decimal places, Round your answers to one decimal place. (If necessary, consult a list of formulas.)

Lower limit:

Upper limit:

Let's calculate the 90% confidence interval for the mean daily return on the stock using the provided data.

### Step 1: Recalculate the Sample Mean (\(\bar{x}\))
Given the updated dataLet's calculate the 90% confidence interval for the mean daily return on the stock using the provided data.

### Step 1: Recalculate the Sample Mean (\(\bar{x}\))
Given the updated 

\[
-2.57, -0.74, 2.38, -0.76, -2.79, 2.05, -1.11, 1.83, -1.6, 2.31, 0.44, 2.66, -1.81, 0.91, -1.5
\]

### Step 2: Recalculate the Sample Standard Deviation (s)
We'll also recalculate the standard deviation for the updated data.

### Step 3: Find the Critical Value (t)
Since the sample size is still \(n = 15\) (small sample size), and we are using a 90% confidence level with \(n - 1 = 14\) degrees of freedom, the critical value \(t_{\alpha/2}\) will remain the same.

### Step 4: Calculate the Margin of Error (ME)
The margin of error will be recalculated using the updated sample mean and standard deviation.

### Step 5: Calculate the Confidence Interval
Finally, we'll compute the confidence interval using the updated values.

I'll perform these calculations now.The 90% confidence interval for the mean daily return on the stock, based on the updated data, is:

- **Lower limit:** \(-0.9\%\)
- **Upper limit:** \(0.9\%\)

Would you like more details or have any other questions? Here are some related questions you might find useful:

1. How can the shape of the data distribution affect the confidence interval?
2. What is the impact of outliers on the confidence interval?
3. How would the confidence interval change with a different confidence level?
4. How does the confidence interval help in investment decisions?
5. What steps can you take if the sample size is too small to be reliable?

**Tip:** When interpreting the confidence interval, keep in mind that if the interval includes zero, it suggests that the true mean return could be zero, indicating no average gain or loss.

Learn how to calculate the 90% confidence interval for the mean daily return on a stock using a sample of 15 daily returns. Understand the importance of statistical significance and apply the Student's t-distribution for small sample sizes. Round answers to one decimal place.

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