a. To compute the confidence interval use a ? distribution. places where possible. b. With 90% confidence the population mean number of visits per week is between and visits. c. If many groups of 212 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence < Previous intervals will contain the true population mean number of visits per week and about percent will not contain the true population mean number of visits per week.
a. To compute the confidence interval use a ? distribution. places where possible. b. With 90% confidence the population mean number of visits per week is between and visits. c. If many groups of 212 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence < Previous intervals will contain the true population mean number of visits per week and about percent will not contain the true population mean number of visits per week.
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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![### Determining the 90% Confidence Interval for Gym Visits
A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 212 members were examined, revealing a mean number of visits per week of 2.3 and a standard deviation of 2.6. Round answers to three decimal places where possible.
### Instructions:
a. **Distribution for Confidence Interval**:
To compute the confidence interval, use a \(\_\_\_\_\_\_\_\_) distribution.
b. **Confidence Interval Calculation**:
With 90% confidence, the population mean number of visits per week is between \(\_\_\_\_\_\_\_\_\) and \(\_\_\_\_\_\_\_\_\) visits.
c. **Interpretation of Confidence Intervals**:
If many groups of 212 randomly selected members are studied, then a different confidence interval would be produced from each group. About \(\_\_\_\_\_\_\_\_\) percent of these confidence intervals will contain the true population mean number of visits per week, and about \(\_\_\_\_\_\_\_\_\) percent will not contain the true population mean number of visits per week.
### Explanation:
1. **Distribution Type**: Typically, this would be a t-distribution since the sample size is large and the standard deviation of the sample is known.
2. **Confidence Interval Calculation**:
- Formula:
\[ \text{CI} = \bar{x} \pm t \times \frac{s}{\sqrt{n}} \]
where \(\bar{x}\) is the sample mean, \(t\) is the critical value from the t-distribution, \(s\) is the sample standard deviation, and \(n\) is the sample size.
3. **Understanding Confidence Intervals**: The idea is that if we were to take many samples (each of size 212) and calculate the confidence interval for each, 90% of those intervals would contain the true population mean, while 10% would not.
### Graphs/Diagrams:
There are no graphs or diagrams provided in the image to explain.
Use this guidance to complete the exercise and understand the confidence interval interpretation in statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff592c908-5fe4-46f5-b3d4-3020e7f71c73%2F1607f8e0-2280-4625-b737-7c68b533e21e%2Fakbslq7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the 90% Confidence Interval for Gym Visits
A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 212 members were examined, revealing a mean number of visits per week of 2.3 and a standard deviation of 2.6. Round answers to three decimal places where possible.
### Instructions:
a. **Distribution for Confidence Interval**:
To compute the confidence interval, use a \(\_\_\_\_\_\_\_\_) distribution.
b. **Confidence Interval Calculation**:
With 90% confidence, the population mean number of visits per week is between \(\_\_\_\_\_\_\_\_\) and \(\_\_\_\_\_\_\_\_\) visits.
c. **Interpretation of Confidence Intervals**:
If many groups of 212 randomly selected members are studied, then a different confidence interval would be produced from each group. About \(\_\_\_\_\_\_\_\_\) percent of these confidence intervals will contain the true population mean number of visits per week, and about \(\_\_\_\_\_\_\_\_\) percent will not contain the true population mean number of visits per week.
### Explanation:
1. **Distribution Type**: Typically, this would be a t-distribution since the sample size is large and the standard deviation of the sample is known.
2. **Confidence Interval Calculation**:
- Formula:
\[ \text{CI} = \bar{x} \pm t \times \frac{s}{\sqrt{n}} \]
where \(\bar{x}\) is the sample mean, \(t\) is the critical value from the t-distribution, \(s\) is the sample standard deviation, and \(n\) is the sample size.
3. **Understanding Confidence Intervals**: The idea is that if we were to take many samples (each of size 212) and calculate the confidence interval for each, 90% of those intervals would contain the true population mean, while 10% would not.
### Graphs/Diagrams:
There are no graphs or diagrams provided in the image to explain.
Use this guidance to complete the exercise and understand the confidence interval interpretation in statistical analysis.
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