Also need margin of error. **Transcription for Educational Website**---**Title: Confidence Interval and Margin of Error Calculation**In a random sample of 29 people, the mean commute time to work was 34.5 minutes, and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a t-distribution to construct a 98% confidence interval for the population mean $ \mu $. What is the margin of error of $ \mu $? Interpret the results.**The confidence interval for the population mean $ \mu $ is $(\_\_\_, \_\_\_)$.** (Round to one decimal place as needed.)---In this scenario, we are tasked with finding a confidence interval for the average commute time using a sample mean, sample standard deviation, and a specified confidence level. The confidence interval will give us a range within which we can be 98% confident that the true population mean lies.To calculate the margin of error and the confidence interval, we typically follow these steps:1. **Determine the sample mean ($\bar{x}$) and standard deviation (s):** - Sample mean ($\bar{x}$) = 34.5 minutes - Standard deviation (s) = 7.2 minutes2. **Identify the sample size (n):** - Sample size (n) = 293. **Find the t-value for a 98% confidence level using a t-distribution table.** The degrees of freedom (df) would be $ n - 1 = 28 $.4. **Calculate the margin of error (ME):** - Formula: $ ME = t \times \frac{s}{\sqrt{n}} $5. **Determine the confidence interval using the formula:** - Confidence interval = $ \bar{x} \pm ME $Interpret the results: This will show the interval in which the true mean commute time for the population is likely to lie with 98% confidence.

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distributed and use a t-distribution to construct a 98% confidence interval for the population mean µ. What is the margin of error of µ? Interpret the results.

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

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Also need margin of error.

**Transcription for Educational Website**

---

**Title: Confidence Interval and Margin of Error Calculation**

In a random sample of 29 people, the mean commute time to work was 34.5 minutes, and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a t-distribution to construct a 98% confidence interval for the population mean $ \mu $. What is the margin of error of $ \mu $? Interpret the results.

**The confidence interval for the population mean $ \mu $ is $(\_\_\_, \_\_\_)$.**
(Round to one decimal place as needed.)

---

In this scenario, we are tasked with finding a confidence interval for the average commute time using a sample mean, sample standard deviation, and a specified confidence level. The confidence interval will give us a range within which we can be 98% confident that the true population mean lies.

To calculate the margin of error and the confidence interval, we typically follow these steps:

1. **Determine the sample mean ($\bar{x}$) and standard deviation (s):**
- Sample mean ($\bar{x}$) = 34.5 minutes
- Standard deviation (s) = 7.2 minutes

2. **Identify the sample size (n):**
- Sample size (n) = 29

3. **Find the t-value for a 98% confidence level using a t-distribution table.** The degrees of freedom (df) would be $ n - 1 = 28 $.

4. **Calculate the margin of error (ME):**
- Formula: $ ME = t \times \frac{s}{\sqrt{n}} $

5. **Determine the confidence interval using the formula:**
- Confidence interval = $ \bar{x} \pm ME $

Interpret the results: This will show the interval in which the true mean commute time for the population is likely to lie with 98% confidence.

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