Construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed. c=0.90, x= 12.4, s=0.76, n=18 (Round to one decimal place as needed.)
Construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed. c=0.90, x= 12.4, s=0.76, n=18 (Round to one decimal place as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Constructing a Confidence Interval for the Population Mean**
In this exercise, we aim to construct the indicated confidence interval for the population mean \( \mu \) using the t-distribution, given that the population is normally distributed.
**Given Data:**
- Confidence Level (\( c \)): 0.90
- Sample Mean (\( \bar{x} \)): 12.4
- Sample Standard Deviation (\( s \)): 0.76
- Sample Size (\( n \)): 18
**Task:**
Calculate the confidence interval and round your final answer to one decimal place.
**Calculation Steps:**
1. **Determine the Degrees of Freedom (df):**
\[
df = n - 1 = 18 - 1 = 17
\]
2. **Find the Critical t-value (\( t^{*} \)):**
For a confidence level of 0.90 and df = 17, use a t-distribution table or calculator to find \( t^{*} \).
3. **Calculate the Standard Error (SE):**
\[
SE = \frac{s}{\sqrt{n}} = \frac{0.76}{\sqrt{18}}
\]
4. **Construct the Confidence Interval:**
\[
\bar{x} \pm t^{*} \times SE
\]
Insert the calculated values and complete the confidence interval rounded to one decimal place.
**Answer Section:**
\[ (\_, \_) \]
(Round to one decimal place as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38aa5034-1eec-4964-a430-19a44c4ef4d5%2Fb3ee80e1-d130-46d9-b281-6f9488c00c1d%2Fsaghxr_processed.png&w=3840&q=75)
Transcribed Image Text:**Constructing a Confidence Interval for the Population Mean**
In this exercise, we aim to construct the indicated confidence interval for the population mean \( \mu \) using the t-distribution, given that the population is normally distributed.
**Given Data:**
- Confidence Level (\( c \)): 0.90
- Sample Mean (\( \bar{x} \)): 12.4
- Sample Standard Deviation (\( s \)): 0.76
- Sample Size (\( n \)): 18
**Task:**
Calculate the confidence interval and round your final answer to one decimal place.
**Calculation Steps:**
1. **Determine the Degrees of Freedom (df):**
\[
df = n - 1 = 18 - 1 = 17
\]
2. **Find the Critical t-value (\( t^{*} \)):**
For a confidence level of 0.90 and df = 17, use a t-distribution table or calculator to find \( t^{*} \).
3. **Calculate the Standard Error (SE):**
\[
SE = \frac{s}{\sqrt{n}} = \frac{0.76}{\sqrt{18}}
\]
4. **Construct the Confidence Interval:**
\[
\bar{x} \pm t^{*} \times SE
\]
Insert the calculated values and complete the confidence interval rounded to one decimal place.
**Answer Section:**
\[ (\_, \_) \]
(Round to one decimal place as needed.)
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