Internet Viewing A researcher wishes to estimate the average number of minutes per day a person spends on the Internet. How large a sample must she select if she wishes to be 99% confident that the population mean is within 11 minutes of the sample mean? Assume the population standard deviation is 36 minutes. Round your final answer up to the next whole number. The researcher needs a sample of at least people.
Internet Viewing A researcher wishes to estimate the average number of minutes per day a person spends on the Internet. How large a sample must she select if she wishes to be 99% confident that the population mean is within 11 minutes of the sample mean? Assume the population standard deviation is 36 minutes. Round your final answer up to the next whole number. The researcher needs a sample of at least people.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![### Internet Viewing Survey
#### Research Objective
A researcher is aiming to estimate the average time (in minutes) a person spends daily on the internet. The goal is to achieve a high degree of confidence in the estimate provided by the sample mean.
#### Key Requirements
1. **Confidence Level**: The researcher wants to be 99% confident in the estimate.
2. **Margin of Error**: The population mean should be within 11 minutes of the sample mean.
3. **Population Standard Deviation**: It is given that the standard deviation is 36 minutes.
#### Sample Size Calculation
To achieve the desired confidence level and margin of error, the researcher needs to determine the appropriate sample size.
#### Result
The researcher needs a sample of at least **\[ \text{in the box} \]** people to meet the criteria.
#### Graphs and Diagrams
There is a text box asking for the sample size. The equation or formula used to derive the sample size is not presented in the image, but typically, sample size calculations in this context use the following formula:
\[ n = \left( \frac{Z \times \sigma}{E} \right)^2 \]
where:
- \( n \) is the sample size
- \( Z \) is the Z-score corresponding to the desired confidence level (for 99%, \( Z \approx 2.576 \))
- \( \sigma \) is the population standard deviation (36 minutes in this case)
- \( E \) is the desired margin of error (11 minutes)
Please ensure all calculations and justifications consider the specified assumptions and requirements.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F176f32ac-c9e1-4f00-8dba-82b002b2f053%2Fe9e1483f-c418-46b0-84ad-72914248fe8a%2F11usoge_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Internet Viewing Survey
#### Research Objective
A researcher is aiming to estimate the average time (in minutes) a person spends daily on the internet. The goal is to achieve a high degree of confidence in the estimate provided by the sample mean.
#### Key Requirements
1. **Confidence Level**: The researcher wants to be 99% confident in the estimate.
2. **Margin of Error**: The population mean should be within 11 minutes of the sample mean.
3. **Population Standard Deviation**: It is given that the standard deviation is 36 minutes.
#### Sample Size Calculation
To achieve the desired confidence level and margin of error, the researcher needs to determine the appropriate sample size.
#### Result
The researcher needs a sample of at least **\[ \text{in the box} \]** people to meet the criteria.
#### Graphs and Diagrams
There is a text box asking for the sample size. The equation or formula used to derive the sample size is not presented in the image, but typically, sample size calculations in this context use the following formula:
\[ n = \left( \frac{Z \times \sigma}{E} \right)^2 \]
where:
- \( n \) is the sample size
- \( Z \) is the Z-score corresponding to the desired confidence level (for 99%, \( Z \approx 2.576 \))
- \( \sigma \) is the population standard deviation (36 minutes in this case)
- \( E \) is the desired margin of error (11 minutes)
Please ensure all calculations and justifications consider the specified assumptions and requirements.
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