Follow PANIC acronym ### Confidence Interval Estimation for Population MeanA NAPA Auto Parts supplier wants information about how long car owners plan to keep their cars. A random sample of 35 car owners results in a sample average of 7.01 years and a standard deviation of 3.74 years. Assume that the sample is drawn from a normally distributed population.Find a 95% confidence interval estimate of the population mean.### Step-by-Step Approach: PANIC#### **P – PARAMETER**Describe the parameter in context. This should be a complete sentence.- **Context**: The parameter is the average number of years that car owners plan to keep their cars. #### **A – ASSUMPTIONS**Are we allowed to construct an interval and why?- **Justification**: We can construct a confidence interval since the sample size is 35, which is greater than 30, making the Central Limit Theorem applicable. Additionally, it is given that the sample is drawn from a normally distributed population.#### **N – NAME THE INTERVAL**State what command you will be using to compute the interval along with the values you need.- **Command**: We will use the formula for a confidence interval for the population mean:\[ \bar{x} \pm t^* \left(\frac{s}{\sqrt{n}}\right) \]where $ \bar{x} $ is the sample mean, $ s $ is the sample standard deviation, $ n $ is the sample size, and $ t^* $ is the critical value from the t-distribution for 95% confidence.#### **I – INTERVAL CALCULATION**Find the interval.1. **Sample Mean ($ \bar{x} $)**: 7.01 years2. **Sample Standard Deviation ($ s $)**: 3.74 years3. **Sample Size ($ n $)**: 354. **Degrees of Freedom (df)**: $ n - 1 = 34 $5. **Critical Value ($ t^* $)**: The critical t-value for 34 degrees of freedom at a 95% confidence level can be found using a t-table or calculator, approximately 2.032.Using the formula:\[ 7.01 \pm 2.032 \left(\frac{3.74}{\sqrt{35}}\right) \]

Name: Follow PANIC acronym ### Confidence Interval Estimation for Population
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Description: Follow PANIC acronym ### Confidence Interval Estimation for Population MeanA NAPA Auto Parts supplier wants information about how long car owners plan to keep their cars. A random sample of 35 car owners results in a sample average of 7.01 years and

Confidence interval gives a range of values for the unknown parameter of the population. The width…

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A NAPA Auto Parts supplier wants information about how long car owner plan to keep their cars. A random sample of 35 car owners results in a sample average of 7.01 years and a standard deviations of 3.74 years. Assume that the sample is drawn from a normally distributed population. Find a 95% confidence interval estimate of the population mean • P- PARAMETER o Describe the parameter in context. This should be a complete sentence • A- ASSUMPTIONS o Are we allowed to construct an interval and why? • N- NAME THE INTERVAL o State what command you will be using the compute the interval along with the values you need. • 1 - INTERVAL CALCULATION o Find the interval C- CONCLUSION

A NAPA Auto Parts supplier wants information about how long car owner plan to keep their cars. A random sample of 35 car owners results in a sample average of 7.01 years and a standard deviations of 3.74 years. Assume that the sample is drawn from a normally distributed population. Find a 95% confidence interval estimate of the population mean • P- PARAMETER o Describe the parameter in context. This should be a complete sentence • A- ASSUMPTIONS o Are we allowed to construct an interval and why? • N- NAME THE INTERVAL o State what command you will be using the compute the interval along with the values you need. • 1 - INTERVAL CALCULATION o Find the interval C- CONCLUSION

MATLAB: An Introduction with Applications

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Author:Amos Gilat

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Binomial Distribution

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Question

Follow PANIC acronym

### Confidence Interval Estimation for Population Mean

A NAPA Auto Parts supplier wants information about how long car owners plan to keep their cars. A random sample of 35 car owners results in a sample average of 7.01 years and a standard deviation of 3.74 years. Assume that the sample is drawn from a normally distributed population.

Find a 95% confidence interval estimate of the population mean.

### Step-by-Step Approach: PANIC

#### **P – PARAMETER**
Describe the parameter in context. This should be a complete sentence.
- **Context**: The parameter is the average number of years that car owners plan to keep their cars.

#### **A – ASSUMPTIONS**
Are we allowed to construct an interval and why?
- **Justification**: We can construct a confidence interval since the sample size is 35, which is greater than 30, making the Central Limit Theorem applicable. Additionally, it is given that the sample is drawn from a normally distributed population.

#### **N – NAME THE INTERVAL**
State what command you will be using to compute the interval along with the values you need.
- **Command**: We will use the formula for a confidence interval for the population mean:
\[ \bar{x} \pm t^* \left(\frac{s}{\sqrt{n}}\right) \]
where $ \bar{x} $ is the sample mean, $ s $ is the sample standard deviation, $ n $ is the sample size, and $ t^* $ is the critical value from the t-distribution for 95% confidence.

#### **I – INTERVAL CALCULATION**
Find the interval.
1. **Sample Mean ($ \bar{x} $)**: 7.01 years
2. **Sample Standard Deviation ($ s $)**: 3.74 years
3. **Sample Size ($ n $)**: 35
4. **Degrees of Freedom (df)**: $ n - 1 = 34 $
5. **Critical Value ($ t^* $)**: The critical t-value for 34 degrees of freedom at a 95% confidence level can be found using a t-table or calculator, approximately 2.032.

Using the formula:
\[ 7.01 \pm 2.032 \left(\frac{3.74}{\sqrt{35}}\right) \]

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