Construct the indicated confidence interval for the population meanu using the t-distribution. Assume the population is normally distributed. c= 0.90, x= 13.9, s=0.73, n= 19 .... (Round to one decimal place as needed.) Help me solve this View an example Get more help - P O Type here to search

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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**Constructing a Confidence Interval for the Population Mean**

To construct a confidence interval for the population mean \(\mu\) using the t-distribution, follow these steps. Assume the population is normally distributed.

**Given:**
- Confidence level (\(c\)): 0.90
- Sample mean (\(\bar{x}\)): 13.9
- Sample standard deviation (\(s\)): 0.73
- Sample size (\(n\)): 19

**Goal:**
- Calculate the confidence interval.

**Instructions:**
1. **Identify the critical value** for the t-distribution using the confidence level and degrees of freedom (\(df = n - 1 = 18\)).

2. **Calculate the standard error** of the mean:
   \[
   SE = \frac{s}{\sqrt{n}}
   \]

3. **Construct the confidence interval**:
   \[
   \bar{x} \pm (t \times SE)
   \]

**Note:** Round the final answers to one decimal place as needed.

**Additional Resources:**
- Use the options "Help me solve this," "View an example," or "Get more help" for guided instruction and further understanding.

**Technical Note:**
Ensure your device's temperature remains optimal to facilitate smooth calculations.
Transcribed Image Text:**Constructing a Confidence Interval for the Population Mean** To construct a confidence interval for the population mean \(\mu\) using the t-distribution, follow these steps. Assume the population is normally distributed. **Given:** - Confidence level (\(c\)): 0.90 - Sample mean (\(\bar{x}\)): 13.9 - Sample standard deviation (\(s\)): 0.73 - Sample size (\(n\)): 19 **Goal:** - Calculate the confidence interval. **Instructions:** 1. **Identify the critical value** for the t-distribution using the confidence level and degrees of freedom (\(df = n - 1 = 18\)). 2. **Calculate the standard error** of the mean: \[ SE = \frac{s}{\sqrt{n}} \] 3. **Construct the confidence interval**: \[ \bar{x} \pm (t \times SE) \] **Note:** Round the final answers to one decimal place as needed. **Additional Resources:** - Use the options "Help me solve this," "View an example," or "Get more help" for guided instruction and further understanding. **Technical Note:** Ensure your device's temperature remains optimal to facilitate smooth calculations.
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