A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, ×, is foundto be 110, and the sample standard deviation, s, is found to be 8.(a) Construct a 99% confidence interval about u if the sample size, n, is 24.(b) Construct a 99% confidence interval about u if the sample size, n, is 13.(c) Construct a 96% confidence interval about u if the sample size, n, is 24.(d) Should the confidence intervals in parts (a)(c) have been computed if the population had not been normallydistributed?An example was provided with additional pictures. **Transcription for Educational Website**A simple random sample of size \( n \) is drawn from a population that is normally distributed. The sample mean, \( \bar{x} \), is found to be 110, and the sample standard deviation, \( s \), is found to be 8.(a) Construct a 99% confidence interval about \( \mu \) if the sample size, \( n \), is 24.(b) Construct a 99% confidence interval about \( \mu \) if the sample size, \( n \), is 13.(c) Construct a 96% confidence interval about \( \mu \) if the sample size, \( n \), is 24.(d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed?---(a) Construct a 99% confidence interval about \( \mu \) if the sample size, \( n \), is 24.- Lower bound: [ ]- Upper bound: [ ]*(Round to one decimal place as needed.)***Additional Image Information:**- No graphs or diagrams are present in the image.- The source or platform is identified as Pearson, providing educational resources. **Confidence Interval Analysis**A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, \( \bar{x} \), is found to be 106, and the sample standard deviation, s, is 12.**Tasks:**(a) Construct a 95% confidence interval about \( \mu \) if the sample size, n, is 23. - **Lower bound:** 100.8 - **Upper bound:** 111.2 - *(Rounded to one decimal place as needed)*(b) Construct a 95% confidence interval about \( \mu \) if the sample size, n, is 13. - **Lower bound:** 98.7 - **Upper bound:** 113.3 - *(Rounded to one decimal place as needed)***Question:**How does decreasing the sample size affect the margin of error, E? - A. As the sample size decreases, the margin of error stays the same. - B. As the sample size decreases, the margin of error decreases. - C. As the sample size decreases, the margin of error increases.**Correct Answer:** C. As the sample size decreases, the margin of error increases.(c) Construct a 90% confidence interval about \( \mu \) if the sample size, n, is 23. - **Lower bound:** 102.7 - **Upper bound:** 109.3(d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed?---This content helps learners understand how confidence intervals are calculated and the effect of sample size on the margin of error.

Answered: Image /qna-images/answer/ede0f614-45d9-4656-acfb-1a3d60ae1772.jpg (d) No!, in order to apply the t-distribution the population as to be normally distributed. This is an assumption of the t-distribution. Note: To calculate the critical t-score use the excel function T.INVα, df.

Answered: A simple random sample of size n is…

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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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, ×, is found to be 110, and the sample standard deviation, s, is found to be 8. (a) Construct a 99% confidence interval about u if the sample size, n, is 24. (b) Construct a 99% confidence interval about u if the sample size, n, is 13. (c) Construct a 96% confidence interval about u if the sample size, n, is 24. (d) Should the confidence intervals in parts (a)(c) have been computed if the population had not been normally distributed? An example was provided with additional pictures.

**Transcription for Educational Website**

A simple random sample of size \( n \) is drawn from a population that is normally distributed. The sample mean, \( \bar{x} \), is found to be 110, and the sample standard deviation, \( s \), is found to be 8.

(a) Construct a 99% confidence interval about \( \mu \) if the sample size, \( n \), is 24.

(b) Construct a 99% confidence interval about \( \mu \) if the sample size, \( n \), is 13.

(c) Construct a 96% confidence interval about \( \mu \) if the sample size, \( n \), is 24.

(d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed?

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(a) Construct a 99% confidence interval about \( \mu \) if the sample size, \( n \), is 24.

- Lower bound: [ ]
- Upper bound: [ ]

*(Round to one decimal place as needed.)*

**Additional Image Information:**

- No graphs or diagrams are present in the image.
- The source or platform is identified as Pearson, providing educational resources.

**Confidence Interval Analysis**

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, \( \bar{x} \), is found to be 106, and the sample standard deviation, s, is 12.

**Tasks:**

(a) Construct a 95% confidence interval about \( \mu \) if the sample size, n, is 23.
- **Lower bound:** 100.8
- **Upper bound:** 111.2
- *(Rounded to one decimal place as needed)*

(b) Construct a 95% confidence interval about \( \mu \) if the sample size, n, is 13.
- **Lower bound:** 98.7
- **Upper bound:** 113.3
- *(Rounded to one decimal place as needed)*

**Question:**

How does decreasing the sample size affect the margin of error, E?

- A. As the sample size decreases, the margin of error stays the same.
- B. As the sample size decreases, the margin of error decreases.
- C. As the sample size decreases, the margin of error increases.

**Correct Answer:** C. As the sample size decreases, the margin of error increases.

(c) Construct a 90% confidence interval about \( \mu \) if the sample size, n, is 23.
- **Lower bound:** 102.7
- **Upper bound:** 109.3

(d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed?

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This content helps learners understand how confidence intervals are calculated and the effect of sample size on the margin of error.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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