MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![### Constructing a Confidence Interval for Mean Attractiveness Ratings
**Study Context:**
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 provided below. The rating scale ranges from 1 to 10, where 1 indicates "not attractive" and 10 indicates "extremely attractive".
**Objective:**
Construct a confidence interval using a 90% confidence level to determine the mean attractiveness ratings of the population of all adult females.
**Sample Data:**
The attractiveness ratings given by male subjects are:
```
8, 9, 3, 9, 7, 4, 6, 8, 9, 9, 6, 8
```
**Question:**
What is the confidence interval for the population mean \( \mu \)?
**Solution Format:**
```
[ ] < μ < [ ]
```
*(Round to one decimal place as needed.)*
**Analysis:**
a. Compute the sample mean (\( \bar{x} \)).
b. Calculate the sample standard deviation (s).
c. Determine the critical value for a 90% confidence interval.
d. Use the formula for the confidence interval:
\[
\bar{x} \pm \left( \text{critical value} \times \frac{s}{\sqrt{n}} \right)
\]
Where:
- \( \bar{x} \) = sample mean
- s = sample standard deviation
- n = number of observations in the sample
- Critical value corresponds to a 90% confidence interval (which can be found using z-tables or t-tables depending on the sample size and distribution).
By completing these calculations, you will determine the confidence interval bounds for the mean attractiveness rating. This allows for an estimation of the typical ratings for the broader population based on the sample data.
Note: Students are encouraged to use statistical software or manual calculations to determine the exact values, ensuring accuracy in results.](https://content.bartleby.com/qna-images/question/77118ecc-eadc-491f-9762-2009f6b89d99/df0b210b-650c-462f-b6ff-3df1ea6113a3/7xe17z.jpeg)
Transcribed Image Text:### Constructing a Confidence Interval for Mean Attractiveness Ratings
**Study Context:**
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 provided below. The rating scale ranges from 1 to 10, where 1 indicates "not attractive" and 10 indicates "extremely attractive".
**Objective:**
Construct a confidence interval using a 90% confidence level to determine the mean attractiveness ratings of the population of all adult females.
**Sample Data:**
The attractiveness ratings given by male subjects are:
```
8, 9, 3, 9, 7, 4, 6, 8, 9, 9, 6, 8
```
**Question:**
What is the confidence interval for the population mean \( \mu \)?
**Solution Format:**
```
[ ] < μ < [ ]
```
*(Round to one decimal place as needed.)*
**Analysis:**
a. Compute the sample mean (\( \bar{x} \)).
b. Calculate the sample standard deviation (s).
c. Determine the critical value for a 90% confidence interval.
d. Use the formula for the confidence interval:
\[
\bar{x} \pm \left( \text{critical value} \times \frac{s}{\sqrt{n}} \right)
\]
Where:
- \( \bar{x} \) = sample mean
- s = sample standard deviation
- n = number of observations in the sample
- Critical value corresponds to a 90% confidence interval (which can be found using z-tables or t-tables depending on the sample size and distribution).
By completing these calculations, you will determine the confidence interval bounds for the mean attractiveness rating. This allows for an estimation of the typical ratings for the broader population based on the sample data.
Note: Students are encouraged to use statistical software or manual calculations to determine the exact values, ensuring accuracy in results.
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