Assuming that the population is normally distributed, construct a 90% confidence interval for the population mean, based on the following sample size of n = 8. 1, 2, 3, 4, 5, 6, 7, and 25 D In the given data, replace the value 25 with 8 and recalculate the confidence interval. Using these results, describe the effect of an outlier (that is, an extreme value) on the confidence interval, in general. Find a 90% confidence interval for the population mean, using the formula or technology.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**Topic: Understanding Confidence Intervals with Outliers**

**Objective:**

- Construct a 90% confidence interval for the population mean with and without an outlier.
- Analyze the impact of an outlier on the confidence interval.

**Data Set:**
- Original data: 1, 2, 3, 4, 5, 6, 7, 25
- Sample size (n) = 8

**Instructions:**

1. **Step 1: Calculate the 90% Confidence Interval**

   Assuming the population is normally distributed, construct the 90% confidence interval for the population mean using the original data set.

2. **Step 2: Modify the Data**

   Replace the outlier (25) with 8 and recalculate the 90% confidence interval. 

3. **Analysis:**

   Describe how the outlier (the extreme value 25) affects the width and position of the confidence interval. Discuss the general impact of outliers.

4. **Technology or Formula:**

   Utilize statistical formulas or technology tools for calculations if required.

**Key Learning Points:**

- Observing changes in confidence intervals with altered data provides insight into the stability of statistical measures against anomalies.
- Recognizing the significance of data integrity in statistical analysis.
Transcribed Image Text:**Topic: Understanding Confidence Intervals with Outliers** **Objective:** - Construct a 90% confidence interval for the population mean with and without an outlier. - Analyze the impact of an outlier on the confidence interval. **Data Set:** - Original data: 1, 2, 3, 4, 5, 6, 7, 25 - Sample size (n) = 8 **Instructions:** 1. **Step 1: Calculate the 90% Confidence Interval** Assuming the population is normally distributed, construct the 90% confidence interval for the population mean using the original data set. 2. **Step 2: Modify the Data** Replace the outlier (25) with 8 and recalculate the 90% confidence interval. 3. **Analysis:** Describe how the outlier (the extreme value 25) affects the width and position of the confidence interval. Discuss the general impact of outliers. 4. **Technology or Formula:** Utilize statistical formulas or technology tools for calculations if required. **Key Learning Points:** - Observing changes in confidence intervals with altered data provides insight into the stability of statistical measures against anomalies. - Recognizing the significance of data integrity in statistical analysis.
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