(a) Provide a 90% confidence interval for the population mean. to (b) Provide a 95% confidence interval for the population mean. to (c) Provide a 99% confidence interval for the population mean. to
(a) Provide a 90% confidence interval for the population mean. to (b) Provide a 95% confidence interval for the population mean. to (c) Provide a 99% confidence interval for the population mean. to
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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![### Confidence Interval Calculation Example
A simple random sample of **50 items** from a population with a **σ = 8** resulted in a sample mean of **34**. (Round your answers to two decimal places.)
#### (a) Provide a 90% confidence interval for the population mean.
\[ \_\_\_\_\_\_\ \text{to} \_\_\_\_\_\_\ ]
#### (b) Provide a 95% confidence interval for the population mean.
\[ \_\_\_\_\_\_\ \ \text{to} \_\_\_\_\_\_\ ]
#### (c) Provide a 99% confidence interval for the population mean.
\[ \_\_\_\_\_\_\ \ \text{to} \_\_\_\_\_\_\ ]
To calculate the confidence intervals, you will need the following information:
- Sample size (n): 50
- Population standard deviation (σ): 8
- Sample mean (x̄): 34
Use the Z-score for the appropriate confidence level:
- For a 90% confidence interval, Z ≈ 1.645
- For a 95% confidence interval, Z ≈ 1.96
- For a 99% confidence interval, Z ≈ 2.576
The formula for the confidence interval is:
\[ \text{CI}_{\%} = \left( x̄ - Z \cdot \frac{σ}{\sqrt{n}}, \ x̄ + Z \cdot \frac{σ}{\sqrt{n}} \right) \]
Plug in the values for each confidence level to find the intervals.
##### Explanation of Confidence Levels:
- **90% Confidence Interval**: This means you can be 90% certain that the population mean falls within this range.
- **95% Confidence Interval**: This means you can be 95% certain that the population mean falls within this range.
- **99% Confidence Interval**: This means you can be 99% certain that the population mean falls within this range.
Insert your calculated lower and upper bounds into the provided blanks.
Feel free to use this structure and calculations for educational purposes to understand the concept of confidence intervals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F928f3826-faea-4936-b5b6-4aab28469498%2Fcdc89c0e-4332-4725-828e-5a4c6de322f0%2F3s1jg94_processed.png&w=3840&q=75)
Transcribed Image Text:### Confidence Interval Calculation Example
A simple random sample of **50 items** from a population with a **σ = 8** resulted in a sample mean of **34**. (Round your answers to two decimal places.)
#### (a) Provide a 90% confidence interval for the population mean.
\[ \_\_\_\_\_\_\ \text{to} \_\_\_\_\_\_\ ]
#### (b) Provide a 95% confidence interval for the population mean.
\[ \_\_\_\_\_\_\ \ \text{to} \_\_\_\_\_\_\ ]
#### (c) Provide a 99% confidence interval for the population mean.
\[ \_\_\_\_\_\_\ \ \text{to} \_\_\_\_\_\_\ ]
To calculate the confidence intervals, you will need the following information:
- Sample size (n): 50
- Population standard deviation (σ): 8
- Sample mean (x̄): 34
Use the Z-score for the appropriate confidence level:
- For a 90% confidence interval, Z ≈ 1.645
- For a 95% confidence interval, Z ≈ 1.96
- For a 99% confidence interval, Z ≈ 2.576
The formula for the confidence interval is:
\[ \text{CI}_{\%} = \left( x̄ - Z \cdot \frac{σ}{\sqrt{n}}, \ x̄ + Z \cdot \frac{σ}{\sqrt{n}} \right) \]
Plug in the values for each confidence level to find the intervals.
##### Explanation of Confidence Levels:
- **90% Confidence Interval**: This means you can be 90% certain that the population mean falls within this range.
- **95% Confidence Interval**: This means you can be 95% certain that the population mean falls within this range.
- **99% Confidence Interval**: This means you can be 99% certain that the population mean falls within this range.
Insert your calculated lower and upper bounds into the provided blanks.
Feel free to use this structure and calculations for educational purposes to understand the concept of confidence intervals.
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