In a random sample of seven people, the mean driving distance to work was 21.7 miles and the standard deviation was 4.8 miles. Assuming the population is normally distributed and using the t-distribution, a 99% confidence interval for the population mean u is (15.0, 28.4) (and the margin of error is 6.7). Through research, it has been found that the population standard deviation of driving distances to work is 4.1. Using the standard normal distribution with the appropriate calculations for a standard deviation that is known, find the margin of error and construct a 99% confidence interval for the population mean u. Interpret and compare the results. Identify the margin of error. (Round to one decimal place as needed.) Construct a 99% confidence interval for the population mean. (Round to one decimal place as needed.) Click to select your answer(s).

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Author:Amos Gilat
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Chapter1: Starting With Matlab
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### Statistical Analysis Exercise

**Task Instructions:**

1. **Identify the Margin of Error:**

   - Provide your results rounded to one decimal place as needed.

2. **Construct a 99% Confidence Interval for the Population Mean:**

   - Ensure all calculations are rounded to one decimal place as necessary.

**Interpret the Results:**

Select the correct option below and fill in the answer box with your choice. (Type an integer or a decimal. Do not round.)

- **Option A:** With ___% of all random samples of seven people from the population will have a mean driving distance to work (in miles) that is between the interval’s endpoints.
  
- **Option B:** With ___% confidence, it can be said that the population mean driving distance to work (in miles) is between the interval’s endpoints.
  
- **Option C:** It can be said that ___% of the population has a driving distance to work (in miles) that is between the interval’s endpoints.
  
- **Option D:** With ___% confidence, it can be said that most driving distances to work (in miles) in the population are between the interval’s endpoints.

**Comparison with t-distribution Results:**

- The new confidence interval is ___ the confidence interval that used the t-distribution and has ___ center.

**Note:** Click to select your answer(s).

---

This exercise aims to help students understand the concepts of confidence intervals and how to construct and interpret them in statistical analyses.
Transcribed Image Text:### Statistical Analysis Exercise **Task Instructions:** 1. **Identify the Margin of Error:** - Provide your results rounded to one decimal place as needed. 2. **Construct a 99% Confidence Interval for the Population Mean:** - Ensure all calculations are rounded to one decimal place as necessary. **Interpret the Results:** Select the correct option below and fill in the answer box with your choice. (Type an integer or a decimal. Do not round.) - **Option A:** With ___% of all random samples of seven people from the population will have a mean driving distance to work (in miles) that is between the interval’s endpoints. - **Option B:** With ___% confidence, it can be said that the population mean driving distance to work (in miles) is between the interval’s endpoints. - **Option C:** It can be said that ___% of the population has a driving distance to work (in miles) that is between the interval’s endpoints. - **Option D:** With ___% confidence, it can be said that most driving distances to work (in miles) in the population are between the interval’s endpoints. **Comparison with t-distribution Results:** - The new confidence interval is ___ the confidence interval that used the t-distribution and has ___ center. **Note:** Click to select your answer(s). --- This exercise aims to help students understand the concepts of confidence intervals and how to construct and interpret them in statistical analyses.
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