An article reported that for a sample of 54 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO₂ level (ppm) was 654.16, and the sample standard deviation was 163.36. (a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO₂ level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.) 631.92 X ppm Interpret the resulting interval. O We are 95% confident that this interval does not contain the true population mean. We are 95% confident that this interval contains the true population mean. O We are 95% confident that the true population mean lies above this interval. O We are 95% confident that the true population mean lies below this interval. (b) Suppose the investigators had made a rough guess of 172 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 51 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.) kitchens
An article reported that for a sample of 54 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO₂ level (ppm) was 654.16, and the sample standard deviation was 163.36. (a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO₂ level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.) 631.92 X ppm Interpret the resulting interval. O We are 95% confident that this interval does not contain the true population mean. We are 95% confident that this interval contains the true population mean. O We are 95% confident that the true population mean lies above this interval. O We are 95% confident that the true population mean lies below this interval. (b) Suppose the investigators had made a rough guess of 172 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 51 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.) kitchens
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![### Statistical Analysis of CO₂ Levels in Kitchens with Gas Appliances
An article reported data for a sample of 54 kitchens with gas cooking appliances. Over a one-week monitoring period, the sample mean CO₂ level was 654.16 ppm, and the sample standard deviation was 163.36 ppm.
#### (a) Confidence Interval Calculation
Calculate and interpret a 95% confidence interval for the true average CO₂ level in the population of all homes with gas appliances.
- **Confidence Interval Formula**:
\[
\left(631.92, \text{upper limit value to be calculated}\right) \text{ ppm}
\]
- **Interpretation of the Interval**:
- **Selected Option**: "We are 95% confident that this interval contains the true population mean."
This means that if we were to take many samples and build a confidence interval from each, approximately 95% of those intervals would contain the true population mean CO₂ level.
#### (b) Sample Size Determination
Suppose the investigators estimated the standard deviation (\(s\)) as 172 ppm before data collection. Determine the necessary sample size to obtain an interval width of 51 ppm for a 95% confidence level.
- **Solution Format**:
- Required sample size: \([ \text{Calculated Number} ]\) kitchens
This step involves using a standard formula for sample size calculation to ensure the desired precision of the interval width at the specified confidence level.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4927fb7d-fe4d-496e-94ae-b9c9f1ed73cb%2Fd42817ef-5b15-4eb0-ab47-dcc1af564b1d%2Ftw7jz5_processed.png&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of CO₂ Levels in Kitchens with Gas Appliances
An article reported data for a sample of 54 kitchens with gas cooking appliances. Over a one-week monitoring period, the sample mean CO₂ level was 654.16 ppm, and the sample standard deviation was 163.36 ppm.
#### (a) Confidence Interval Calculation
Calculate and interpret a 95% confidence interval for the true average CO₂ level in the population of all homes with gas appliances.
- **Confidence Interval Formula**:
\[
\left(631.92, \text{upper limit value to be calculated}\right) \text{ ppm}
\]
- **Interpretation of the Interval**:
- **Selected Option**: "We are 95% confident that this interval contains the true population mean."
This means that if we were to take many samples and build a confidence interval from each, approximately 95% of those intervals would contain the true population mean CO₂ level.
#### (b) Sample Size Determination
Suppose the investigators estimated the standard deviation (\(s\)) as 172 ppm before data collection. Determine the necessary sample size to obtain an interval width of 51 ppm for a 95% confidence level.
- **Solution Format**:
- Required sample size: \([ \text{Calculated Number} ]\) kitchens
This step involves using a standard formula for sample size calculation to ensure the desired precision of the interval width at the specified confidence level.
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