) What conditions are necessary for your calculations? (Select all that apply.) O uniform distribution of x ✓o is unknown □o is known ✔normal distribution of x ) Find a 90% confidence interval for μ. What is the margin of error? (Round your answers to two d wer limit Oper limit argin of error 0.807 Interpret your results in the context of this problem. obability that this interval contains the true average is 0.80. is a 90% chance that the interval is one of the intervals containing the true average.
) What conditions are necessary for your calculations? (Select all that apply.) O uniform distribution of x ✓o is unknown □o is known ✔normal distribution of x ) Find a 90% confidence interval for μ. What is the margin of error? (Round your answers to two d wer limit Oper limit argin of error 0.807 Interpret your results in the context of this problem. obability that this interval contains the true average is 0.80. is a 90% chance that the interval is one of the intervals containing the true average.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Suppose x has a
![### Statistics Problem Explanation
#### Problem Statement
Suppose \( x \) has a normal distribution with \( s = 1.7 \). A random sample of size 12 has a sample mean of \( \bar{x} = 50 \).
#### Part (a): Conditions for Calculations
**Question:** What conditions are necessary for your calculations? (Select all that apply.)
- \(\square\) Uniform distribution of \( x \)
- \(\checked\) \( \sigma \) is unknown
- \(\square\) \( \sigma \) is known
- \(\checked\) Normal distribution of \( x \)
**Explanation:** For the calculations to be valid, we need to assume that the original population \( x \) follows a normal distribution and that the population standard deviation \( \sigma \) is unknown.
#### Part (b): 90% Confidence Interval
**Question:** Find a 90% confidence interval for \( \mu \). What is the margin of error? (Round your answers to two decimal places.)
- Lower limit: [Text box for input]
- Upper limit: [Text box for input]
- Margin of error: **0.807** (This value is given and marked with a red cross, indicating it is incorrect)
**Explanation:** To find the correct 90% confidence interval and margin of error, we typically use the formula
\[ \text{Margin of Error} = t_{\alpha/2, n-1} \times \frac{s}{\sqrt{n}} \]
where \( t_{\alpha/2, n-1} \) is the t-value from Student’s t-distribution, \( s \) is the sample standard deviation, and \( n \) is the sample size.
#### Part (c): Interpretation
**Question:** Interpret your results in the context of this problem.
- \(\bigcirc\) The probability that this interval contains the true average is 0.80.
- \(\checked\) There is a 90% chance that the interval includes the true average.
- \(\bigcirc\) The probability that this interval contains the true average is 0.20.
- \(\bigcirc\) There is a 20% chance that the interval includes the true average.
**Explanation:** The correct interpretation of a 90% confidence interval is that there is a 90% chance that the computed interval from the sample data includes](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe76f06b-a6e5-4577-ae94-392ea27c231a%2F2cece3a2-3d4a-4379-82e8-877906f658b6%2Fhnigmom_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistics Problem Explanation
#### Problem Statement
Suppose \( x \) has a normal distribution with \( s = 1.7 \). A random sample of size 12 has a sample mean of \( \bar{x} = 50 \).
#### Part (a): Conditions for Calculations
**Question:** What conditions are necessary for your calculations? (Select all that apply.)
- \(\square\) Uniform distribution of \( x \)
- \(\checked\) \( \sigma \) is unknown
- \(\square\) \( \sigma \) is known
- \(\checked\) Normal distribution of \( x \)
**Explanation:** For the calculations to be valid, we need to assume that the original population \( x \) follows a normal distribution and that the population standard deviation \( \sigma \) is unknown.
#### Part (b): 90% Confidence Interval
**Question:** Find a 90% confidence interval for \( \mu \). What is the margin of error? (Round your answers to two decimal places.)
- Lower limit: [Text box for input]
- Upper limit: [Text box for input]
- Margin of error: **0.807** (This value is given and marked with a red cross, indicating it is incorrect)
**Explanation:** To find the correct 90% confidence interval and margin of error, we typically use the formula
\[ \text{Margin of Error} = t_{\alpha/2, n-1} \times \frac{s}{\sqrt{n}} \]
where \( t_{\alpha/2, n-1} \) is the t-value from Student’s t-distribution, \( s \) is the sample standard deviation, and \( n \) is the sample size.
#### Part (c): Interpretation
**Question:** Interpret your results in the context of this problem.
- \(\bigcirc\) The probability that this interval contains the true average is 0.80.
- \(\checked\) There is a 90% chance that the interval includes the true average.
- \(\bigcirc\) The probability that this interval contains the true average is 0.20.
- \(\bigcirc\) There is a 20% chance that the interval includes the true average.
**Explanation:** The correct interpretation of a 90% confidence interval is that there is a 90% chance that the computed interval from the sample data includes
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