What is the confidence interval for the population mean μ? <μ< (Round to one decimal place as needed.)
What is the confidence interval for the population mean μ? <μ< (Round to one decimal place as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
27)
![### Confidence Intervals in Speed Dating Study
In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates. The scale used for this rating ranged from 1 (not attractive) to 10 (extremely attractive). The goal is to construct a confidence interval using a 90% confidence level. This interval will help us understand the mean attractiveness rating of the population of all adult females.
The sample results are as follows:
```
6, 7, 1, 9, 6, 6, 7, 8, 9, 10, 6, 8
```
### Task
What is the confidence interval for the population mean μ?
To solve this, use the collected sample data and calculate the confidence interval to be filled in the format below, rounding to one decimal place:
\[ \boxed{\phantom{00}} < \mu < \boxed{\phantom{00}} \]
### Calculations
1. Find the sample mean ( \(\bar{x}\) ):
2. Calculate the sample standard deviation ( \(s\) ):
3. Determine the standard error of the mean ( \(SE\) ):
4. Use the t-distribution to find the critical t-value for a 90% confidence level.
5. Calculate the margin of error ( \(ME\) ):
6. Construct the confidence interval:
\[ \bar{x} - ME < \mu < \bar{x} + ME \]
Please ensure you round your final answers to one decimal place as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49a5c0da-d10b-4c66-9f47-a76740d10419%2Fe75b954f-1f05-4708-8a37-f8dadf31ded2%2Fftcimsd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Confidence Intervals in Speed Dating Study
In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates. The scale used for this rating ranged from 1 (not attractive) to 10 (extremely attractive). The goal is to construct a confidence interval using a 90% confidence level. This interval will help us understand the mean attractiveness rating of the population of all adult females.
The sample results are as follows:
```
6, 7, 1, 9, 6, 6, 7, 8, 9, 10, 6, 8
```
### Task
What is the confidence interval for the population mean μ?
To solve this, use the collected sample data and calculate the confidence interval to be filled in the format below, rounding to one decimal place:
\[ \boxed{\phantom{00}} < \mu < \boxed{\phantom{00}} \]
### Calculations
1. Find the sample mean ( \(\bar{x}\) ):
2. Calculate the sample standard deviation ( \(s\) ):
3. Determine the standard error of the mean ( \(SE\) ):
4. Use the t-distribution to find the critical t-value for a 90% confidence level.
5. Calculate the margin of error ( \(ME\) ):
6. Construct the confidence interval:
\[ \bar{x} - ME < \mu < \bar{x} + ME \]
Please ensure you round your final answers to one decimal place as needed.
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