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?
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Author:Amos Gilat
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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
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