In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Construct a confidence interval using a 95% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult females?
In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Construct a confidence interval using a 95% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult females?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
how can I do this using statcrunch, excel, or a calculator? thank u
![### Confidence Interval for Population Mean
#### Study Background:
In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates. The ratings were on a scale from 1 to 10, where 1 indicates "not attractive" and 10 indicates "extremely attractive". A sample of these ratings is provided below. Your task is to construct a confidence interval for the population mean attractiveness rating using a 95% confidence level and interpret what this tells us about the mean attractiveness ratings of the population of all adult females.
#### Sample Data:
6, 8, 1, 8, 7, 5, 8, 8, 10, 4, 8
#### Confidence Interval Calculation:
Construct a 95% confidence interval for the population mean (μ).
\[ \text{Range for } \mu: \ \_ < \mu < \_ \]
\[ \text{(Round to one decimal place)} \]
#### Instructions for Students:
1. **Data Entry**: Enter the sample data into appropriate statistical software or a calculator to compute the sample mean and standard deviation.
2. **Formula**: Use the formula for the confidence interval for the mean:
\[
\bar{x} \pm Z \left(\frac{s}{\sqrt{n}}\right)
\]
where:
- \(\bar{x}\) is the sample mean
- \(Z\) is the Z-value corresponding to the 95% confidence level (typically 1.96 for a large sample size)
- \(s\) is the sample standard deviation
- \(n\) is the sample size
3. **Calculate**:
- Calculate the sample mean ( \(\bar{x}\) ).
- Calculate the sample standard deviation ( \(s\) ).
- Find the margin of error using \( Z \left(\frac{s}{\sqrt{n}}\right) \).
- Construct the interval by adding and subtracting the margin of error from the sample mean.
4. **Input Your Answer**: Enter your interval limits in the provided fields and click "Check Answer" to verify.
#### Interpretation:
What do the results tell about the mean attractiveness ratings of the population of all adult females?
**Graphical Explanation (if provided in future):**
- **Graph of Sample Distribution**: A histogram or bar graph showing the frequency of each rating in the sample](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F242a0dac-d7d5-4e5c-b656-00cdaf0b077c%2F4be9a7dc-3cc4-4cee-bdb3-7ec465ed7ad3%2Fkkjhyxb.png&w=3840&q=75)
Transcribed Image Text:### Confidence Interval for Population Mean
#### Study Background:
In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates. The ratings were on a scale from 1 to 10, where 1 indicates "not attractive" and 10 indicates "extremely attractive". A sample of these ratings is provided below. Your task is to construct a confidence interval for the population mean attractiveness rating using a 95% confidence level and interpret what this tells us about the mean attractiveness ratings of the population of all adult females.
#### Sample Data:
6, 8, 1, 8, 7, 5, 8, 8, 10, 4, 8
#### Confidence Interval Calculation:
Construct a 95% confidence interval for the population mean (μ).
\[ \text{Range for } \mu: \ \_ < \mu < \_ \]
\[ \text{(Round to one decimal place)} \]
#### Instructions for Students:
1. **Data Entry**: Enter the sample data into appropriate statistical software or a calculator to compute the sample mean and standard deviation.
2. **Formula**: Use the formula for the confidence interval for the mean:
\[
\bar{x} \pm Z \left(\frac{s}{\sqrt{n}}\right)
\]
where:
- \(\bar{x}\) is the sample mean
- \(Z\) is the Z-value corresponding to the 95% confidence level (typically 1.96 for a large sample size)
- \(s\) is the sample standard deviation
- \(n\) is the sample size
3. **Calculate**:
- Calculate the sample mean ( \(\bar{x}\) ).
- Calculate the sample standard deviation ( \(s\) ).
- Find the margin of error using \( Z \left(\frac{s}{\sqrt{n}}\right) \).
- Construct the interval by adding and subtracting the margin of error from the sample mean.
4. **Input Your Answer**: Enter your interval limits in the provided fields and click "Check Answer" to verify.
#### Interpretation:
What do the results tell about the mean attractiveness ratings of the population of all adult females?
**Graphical Explanation (if provided in future):**
- **Graph of Sample Distribution**: A histogram or bar graph showing the frequency of each rating in the sample
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman