In a random sample of 12 American adults, the mean waste recycled per person per day was 1.2 pounds and the standard deviation was 0.3 pound. Assume that the amount of waste recycled is normally distributed. The 90% confidence interval for the population mean is pounds << pounds (Round values to the nearest hundredth. There must be two digits after the decimal point. Do not write the units.)
In a random sample of 12 American adults, the mean waste recycled per person per day was 1.2 pounds and the standard deviation was 0.3 pound. Assume that the amount of waste recycled is normally distributed. The 90% confidence interval for the population mean is pounds << pounds (Round values to the nearest hundredth. There must be two digits after the decimal point. Do not write the units.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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![### Statistics Lesson: Confidence Intervals
In a random sample of 12 American adults, the mean waste recycled per person per day was 1.2 pounds, and the standard deviation was 0.3 pounds. Assume that the amount of waste recycled is normally distributed.
#### Confidence Interval Calculation
To determine the 90% confidence interval for the population mean, use the following formula:
\[ \text{Confidence Interval} = \left( \bar{x} - z \frac{s}{\sqrt{n}}, \, \bar{x} + z \frac{s}{\sqrt{n}} \right) \]
Where:
- \(\bar{x}\) is the sample mean (1.2 pounds).
- \(s\) is the sample standard deviation (0.3 pounds).
- \(n\) is the sample size (12).
- \(z\) is the z-value corresponding to the desired confidence level (for a 90% confidence level, \(z \approx 1.645\)).
### Task:
Complete the 90% confidence interval for the population mean. Ensure to round the values to the nearest hundredth. There must be two digits after the decimal point. Do not write the units.
\[ \text{Confidence Interval} = \left( \boxed{ \, } \, \text{pounds} < \mu < \boxed{ \, } \, \text{pounds} \right) \]
---
Educational Tip:
Understanding how to calculate and interpret confidence intervals is crucial in statistics as it helps to estimate the population parameter and understand the precision and reliability of your sample statistics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdab6bfb8-cb1a-4a62-b8d6-065f4d11ace0%2Fec9baffe-6887-46f9-96f2-223cbc7ccedf%2Ftae1zmt_processed.png&w=3840&q=75)
Transcribed Image Text:### Statistics Lesson: Confidence Intervals
In a random sample of 12 American adults, the mean waste recycled per person per day was 1.2 pounds, and the standard deviation was 0.3 pounds. Assume that the amount of waste recycled is normally distributed.
#### Confidence Interval Calculation
To determine the 90% confidence interval for the population mean, use the following formula:
\[ \text{Confidence Interval} = \left( \bar{x} - z \frac{s}{\sqrt{n}}, \, \bar{x} + z \frac{s}{\sqrt{n}} \right) \]
Where:
- \(\bar{x}\) is the sample mean (1.2 pounds).
- \(s\) is the sample standard deviation (0.3 pounds).
- \(n\) is the sample size (12).
- \(z\) is the z-value corresponding to the desired confidence level (for a 90% confidence level, \(z \approx 1.645\)).
### Task:
Complete the 90% confidence interval for the population mean. Ensure to round the values to the nearest hundredth. There must be two digits after the decimal point. Do not write the units.
\[ \text{Confidence Interval} = \left( \boxed{ \, } \, \text{pounds} < \mu < \boxed{ \, } \, \text{pounds} \right) \]
---
Educational Tip:
Understanding how to calculate and interpret confidence intervals is crucial in statistics as it helps to estimate the population parameter and understand the precision and reliability of your sample statistics.
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