Suppose that a random sample of 16 adult U.S. males has a mean height of 70 inches with a standard deviation of 2 inches. If we assume that the heights of adult males in the U.S. are normally distributed, find a 99% confidence interval for the mean height of all U.S. males. Give the lower limit and upper limit of the 99% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
Suppose that a random sample of 16 adult U.S. males has a mean height of 70 inches with a standard deviation of 2 inches. If we assume that the heights of adult males in the U.S. are normally distributed, find a 99% confidence interval for the mean height of all U.S. males. Give the lower limit and upper limit of the 99% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
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
100%
Lower limit=
Upper Limit=
 of 16 adult U.S. males has a [mean](https://mathworld.wolfram.com/ArithmeticMean.html) height of 70 inches with a [standard deviation](https://mathworld.wolfram.com/StandardDeviation.html) of 2 inches. If we assume that the heights of adult males in the U.S. are [normally distributed](https://mathworld.wolfram.com/NormalDistribution.html), find a 99% [confidence interval](https://mathworld.wolfram.com/ConfidenceInterval.html) for the [mean](https://mathworld.wolfram.com/ArithmeticMean.html) height of all U.S. males. Give the lower limit and upper limit of the 99% confidence interval.
---
**Instructions:**
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a [list of formulas](https://mathworld.wolfram.com/).
---
### Calculation Steps:
1. **Determine the sample mean (\(\bar{x}\)):**
- Given: \(\bar{x} = 70\) inches.
2. **Determine the sample standard deviation (s):**
- Given: \(s = 2\) inches.
3. **Determine the sample size (n):**
- Given: \(n = 16\).
4. **Find the critical value (z) for a 99% confidence interval:**
- Use a Z-table or standard normal distribution table to find \(z\).
- For a 99% confidence level, \(z \approx 2.576\).
5. **Calculate the standard error of the mean (SEM):**
- \( \text{SEM} = \frac{s}{\sqrt{n}} = \frac{2}{\sqrt{16}} = \frac{2}{4} = 0.5 \)
6. **Compute the margin of error (ME):**
- \( \text{ME} = z \times \text{SEM} = 2.576 \times 0.5 = 1.288 \)
7. **Determine the confidence interval:**
- \(\bar{x} \pm \text{ME} =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50a93c10-85d4-41d2-a577-62aadf58513c%2F9079ac75-26fb-4ae9-ab0c-5b968bba79c6%2F9uo0owa_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Content on Confidence Intervals
---
**Problem Statement:**
Suppose that a [random sample](https://mathworld.wolfram.com/RandomSample.html) of 16 adult U.S. males has a [mean](https://mathworld.wolfram.com/ArithmeticMean.html) height of 70 inches with a [standard deviation](https://mathworld.wolfram.com/StandardDeviation.html) of 2 inches. If we assume that the heights of adult males in the U.S. are [normally distributed](https://mathworld.wolfram.com/NormalDistribution.html), find a 99% [confidence interval](https://mathworld.wolfram.com/ConfidenceInterval.html) for the [mean](https://mathworld.wolfram.com/ArithmeticMean.html) height of all U.S. males. Give the lower limit and upper limit of the 99% confidence interval.
---
**Instructions:**
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a [list of formulas](https://mathworld.wolfram.com/).
---
### Calculation Steps:
1. **Determine the sample mean (\(\bar{x}\)):**
- Given: \(\bar{x} = 70\) inches.
2. **Determine the sample standard deviation (s):**
- Given: \(s = 2\) inches.
3. **Determine the sample size (n):**
- Given: \(n = 16\).
4. **Find the critical value (z) for a 99% confidence interval:**
- Use a Z-table or standard normal distribution table to find \(z\).
- For a 99% confidence level, \(z \approx 2.576\).
5. **Calculate the standard error of the mean (SEM):**
- \( \text{SEM} = \frac{s}{\sqrt{n}} = \frac{2}{\sqrt{16}} = \frac{2}{4} = 0.5 \)
6. **Compute the margin of error (ME):**
- \( \text{ME} = z \times \text{SEM} = 2.576 \times 0.5 = 1.288 \)
7. **Determine the confidence interval:**
- \(\bar{x} \pm \text{ME} =
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman