Water Temperature If the variance of the water temperature in a lake is 28°, how many days should the researcher select to measure the temperature to estimate the true mean within 3° with 90% confidence? Round the intermediate calculations to two decimal places and round up your final answer to the next whole number. The researcher needs a sample of at least days.
Water Temperature If the variance of the water temperature in a lake is 28°, how many days should the researcher select to measure the temperature to estimate the true mean within 3° with 90% confidence? Round the intermediate calculations to two decimal places and round up your final answer to the next whole number. The researcher needs a sample of at least days.
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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![**Water Temperature**
If the variance of the water temperature in a lake is 28°, how many days should the researcher select to measure the temperature to estimate the true mean within 3° with 90% confidence? Round the intermediate calculations to two decimal places and round up your final answer to the next whole number.
[The researcher needs a sample of at least ___ days.]
**Explanation:**
- **Variance** is given as 28°.
- **Desired precision** (margin of error) is within 3°.
- **Confidence level** is 90%.
The formula typically used to find the sample size for estimating a mean is derived from the equation for the margin of error in a confidence interval. It may involve the Z-score for 90% confidence, which is approximately 1.645. Calculations would use the formula:
\[ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 \]
Where:
- \( n \) is the sample size.
- \( Z \) is the Z-score for the confidence level.
- \( \sigma \) (standard deviation) is the square root of the variance.
- \( E \) is the desired margin of error.
Calculate \( n \) and round up to the next whole number.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3510745c-b224-4e3c-988a-4a06d65307ae%2Ffb97f38c-9634-4c10-808e-f2232c49813e%2F9sq1tyw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Water Temperature**
If the variance of the water temperature in a lake is 28°, how many days should the researcher select to measure the temperature to estimate the true mean within 3° with 90% confidence? Round the intermediate calculations to two decimal places and round up your final answer to the next whole number.
[The researcher needs a sample of at least ___ days.]
**Explanation:**
- **Variance** is given as 28°.
- **Desired precision** (margin of error) is within 3°.
- **Confidence level** is 90%.
The formula typically used to find the sample size for estimating a mean is derived from the equation for the margin of error in a confidence interval. It may involve the Z-score for 90% confidence, which is approximately 1.645. Calculations would use the formula:
\[ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 \]
Where:
- \( n \) is the sample size.
- \( Z \) is the Z-score for the confidence level.
- \( \sigma \) (standard deviation) is the square root of the variance.
- \( E \) is the desired margin of error.
Calculate \( n \) and round up to the next whole number.
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