https://file.aiquickdraw.com/mathbot/file/17265308162373ht9f52q.jpg

The image shows a question about calculating confidence intervals, both with and without an outlier, from a sample of college freshmen's sleeping hours.

### Part 1: 
- **Question:** Eliminate the outlier (24 hours) and calculate the 95% confidence interval for the mean sleep hours from the remaining data.
- **Answer:** The 95% confidence interval without the outlier is \( 7.27 \leq \mu \leq 9.07 \).

### Part 2: 
- **Question:** Include the outlier and calculate the 95% confidence interval for the mean sleep hours with all data.
- **Answer:** The 95% confidence interval including the outlier is \( 6.01 \leq \mu \leq 13.49 \).

### Part 3:
- **Question:** Are the results noticeably different?
- **Answer:** Likely yes, because the inclusion of the outlier greatly expanded the confidence interval, increasing the upper bound significantly. Thus, it skews the results.

Would you like a deeper explanation of how confidence intervals were calculated? Here are 5 related questions for further exploration:

1. What is the impact of an outlier on the mean of a dataset?
2. How do you calculate the 95% confidence interval for a given dataset?
3. What happens to the width of a confidence interval when variability in the data increases?
4. Why are outliers typically excluded in statistical analysis?
5. Can an outlier affect both the mean and standard deviation equally?

**Tip:** Always review data for outliers, as they can distort statistical measures like the mean and variance.

A simple random sample of ten college freshmen were asked how many hours of sleep they typically got per night. The data included an outlier of 24 hours. The task was to calculate the 95% confidence interval for the mean sleep hours, both with and without the outlier.

Learn how to calculate the 95% confidence interval for sleep hours from a sample of college freshmen, both with and without an outlier. Explore how an outlier affects statistical measures like the mean and confidence intervals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation