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 90% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult females? 5, 7, 2, 8, 6, 5, 6, 8, 7, 8, 5, 9 What is the confidence interval for the population mean u?

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In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, using a scale where 1 equals "not attractive" and 10 equals "extremely attractive." A sample of the results is provided: 5, 7, 2, 8, 6, 5, 6, 8, 7, 8, 5, 9. Based on this data, we are asked to construct a confidence interval using a 90% confidence level. The task is to determine what these results indicate about the mean attractiveness ratings of the population of all adult females.

**Question:**
What is the confidence interval for the population mean \( \mu \)?

\( < \mu < \) 
*(Round to one decimal place as needed.)*

**Interpretation:**
What does the confidence interval tell us about the population of all adult females? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.

- **Option A:** We are confident that 90% of all adult females have attractiveness ratings between \(\_\_\) and \(\_\_\).  
  *(Round to one decimal place as needed.)*

- **Option B:** We are 90% confident that the interval from \(\_\_\) to \(\_\_\) actually contains the true mean attractiveness rating of all adult females.
  *(Round to one decimal place as needed.)*

- **Option C:** The results tell nothing about the population of all adult females, because participants in speed dating are not a representative sample of the population of all adult females.

### Explanation of Confidence Intervals:
A confidence interval provides a range of values that is likely to contain the population mean with a certain level of confidence. In this context, a 90% confidence interval indicates that if the study were repeated multiple times, 90% of the calculated confidence intervals would contain the true mean attractiveness rating of all adult females.

### Note:
The calculation and interpretation of the confidence interval rely on the assumption that the sample is representative of the population. If the sample is biased or not representative, the confidence interval might not be valid.
Transcribed Image Text:In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, using a scale where 1 equals "not attractive" and 10 equals "extremely attractive." A sample of the results is provided: 5, 7, 2, 8, 6, 5, 6, 8, 7, 8, 5, 9. Based on this data, we are asked to construct a confidence interval using a 90% confidence level. The task is to determine what these results indicate about the mean attractiveness ratings of the population of all adult females. **Question:** What is the confidence interval for the population mean \( \mu \)? \( < \mu < \) *(Round to one decimal place as needed.)* **Interpretation:** What does the confidence interval tell us about the population of all adult females? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. - **Option A:** We are confident that 90% of all adult females have attractiveness ratings between \(\_\_\) and \(\_\_\). *(Round to one decimal place as needed.)* - **Option B:** We are 90% confident that the interval from \(\_\_\) to \(\_\_\) actually contains the true mean attractiveness rating of all adult females. *(Round to one decimal place as needed.)* - **Option C:** The results tell nothing about the population of all adult females, because participants in speed dating are not a representative sample of the population of all adult females. ### Explanation of Confidence Intervals: A confidence interval provides a range of values that is likely to contain the population mean with a certain level of confidence. In this context, a 90% confidence interval indicates that if the study were repeated multiple times, 90% of the calculated confidence intervals would contain the true mean attractiveness rating of all adult females. ### Note: The calculation and interpretation of the confidence interval rely on the assumption that the sample is representative of the population. If the sample is biased or not representative, the confidence interval might not be valid.
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