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Construct a 98% confidence interval about if the sample size, n, is 16. Construct a 98% confidence interval about u if the sample size, n, is 26. Construct a 99% confidence interval about u if the sample size, n, is 16. Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Click the icon to view the table of areas under the t-distribution. Construct a 98% confidence interval about u if the sample size, n, is 16. wer bound: Upper bound: se ascending order. Round to one decimal place as needed.)

Construct a 98% confidence interval about if the sample size, n, is 16. Construct a 98% confidence interval about u if the sample size, n, is 26. Construct a 99% confidence interval about u if the sample size, n, is 16. Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Click the icon to view the table of areas under the t-distribution. Construct a 98% confidence interval about u if the sample size, n, is 16. wer bound: Upper bound: se ascending order. Round to one decimal place as needed.)

MATLAB: An Introduction with Applications
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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**Problem Statement:** 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 105, and the sample standard deviation, \( s \), is found to be 10. **Tasks:** (a) Construct a 98% confidence interval about \( \mu \) if the sample size, \( n \), is 16. (b) Construct a 98% confidence interval about \( \mu \) if the sample size, \( n \), is 26. (c) Construct a 99% confidence interval about \( \mu \) if the sample size, \( n \), is 16. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? *Click the icon to view the table of areas under the t-distribution.* --- **Solution for Task (a):** Construct a 98% confidence interval about \( \mu \) if the sample size, \( n \), is 16. - Lower bound: [Input required] - Upper bound: [Input required] (Use ascending order. Round to one decimal place as needed.)
Transcribed Image Text:**Problem Statement:** 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 105, and the sample standard deviation, \( s \), is found to be 10. **Tasks:** (a) Construct a 98% confidence interval about \( \mu \) if the sample size, \( n \), is 16. (b) Construct a 98% confidence interval about \( \mu \) if the sample size, \( n \), is 26. (c) Construct a 99% confidence interval about \( \mu \) if the sample size, \( n \), is 16. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? *Click the icon to view the table of areas under the t-distribution.* --- **Solution for Task (a):** Construct a 98% confidence interval about \( \mu \) if the sample size, \( n \), is 16. - Lower bound: [Input required] - Upper bound: [Input required] (Use ascending order. Round to one decimal place as needed.)
### Table of t-Distribution Areas **Overview Diagram:** The image features a bell curve that illustrates the concept of the t-distribution. The shaded area in the right tail represents the probability for a given t-value, highlighting its significance in statistical calculations. **Table VI: t-Distribution Area in Right Tail** This table provides critical values of the t-distribution corresponding to different areas in the right tail. The columns represent the area in the right tail, while the rows correspond to degrees of freedom (df). | df | 0.25 | 0.20 | 0.15 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.0025 | 0.001 | 0.0005 | |----|-------|-------|-------|-------|-------|-------|-------|-------|-------|--------|--------|--------| | 1 | 1.000 | 1.376 | 1.963 | 3.078 | 6.314 | 12.706| 15.894| 31.821| 63.657| 127.321| 318.309| 636.619| | 2 | 0.816 | 1.061 | 1.386 | 1.886 | 2.920 | 4.303 | 4.849 | 6.965 | 9.925 | 14.089 | 22.327 | 31.599 | | 3 | 0.765 | 0.978 | 1.250 | 1.638 | 2.353 | 3.182 | 3.482 | 4.541 | 5.841 | 7.453 | 10.215 | 12.924 | | 4 | 0.741 | 0.941 | 1.190 | 1.533 | 2.132 | 2.776 | 2.999 | 3.747 | 4.604 | 5.598 | 7.173 | 8.610 | | 5 | 0.727 | 0.920 | 1.156 | 1.476 | 2.015 | 2
Transcribed Image Text:### Table of t-Distribution Areas **Overview Diagram:** The image features a bell curve that illustrates the concept of the t-distribution. The shaded area in the right tail represents the probability for a given t-value, highlighting its significance in statistical calculations. **Table VI: t-Distribution Area in Right Tail** This table provides critical values of the t-distribution corresponding to different areas in the right tail. The columns represent the area in the right tail, while the rows correspond to degrees of freedom (df). | df | 0.25 | 0.20 | 0.15 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.0025 | 0.001 | 0.0005 | |----|-------|-------|-------|-------|-------|-------|-------|-------|-------|--------|--------|--------| | 1 | 1.000 | 1.376 | 1.963 | 3.078 | 6.314 | 12.706| 15.894| 31.821| 63.657| 127.321| 318.309| 636.619| | 2 | 0.816 | 1.061 | 1.386 | 1.886 | 2.920 | 4.303 | 4.849 | 6.965 | 9.925 | 14.089 | 22.327 | 31.599 | | 3 | 0.765 | 0.978 | 1.250 | 1.638 | 2.353 | 3.182 | 3.482 | 4.541 | 5.841 | 7.453 | 10.215 | 12.924 | | 4 | 0.741 | 0.941 | 1.190 | 1.533 | 2.132 | 2.776 | 2.999 | 3.747 | 4.604 | 5.598 | 7.173 | 8.610 | | 5 | 0.727 | 0.920 | 1.156 | 1.476 | 2.015 | 2
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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 105, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about µ if the sample size, n, is 16. μ (b) Construct a 98% confidence interval about µ if the sample size, n, is 26. (c) Construct a 99% confidence interval about u if the sample size, n, is 16. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Click the icon to view the table of areas under the t-distribution. (a) Construct a 98% confidence interval about µ if the sample size, n, is 16. μ Lower bound: 98.5; Upper bound: 111.5 (Use ascending order. Round to one decimal place as needed.) (b) Construct a 98% confidence interval about µ if the sample size, n, is 26. Lower bound: 100.1 ; Upper bound: 109.9 (Use ascending order. Round to one decimal place as needed.) How does increasing the sample size affect the margin of error, E? A. As the sample size increases, the margin of error stays the same. B. As the sample size increases, the margin of error decreases. C. As the sample size increases, the margin of error increases. (c) Construct a 99% confidence interval about µ if the sample size, n, is 16. Lower bound:; Upper bound: (Use ascending order. Round to one decimal place as needed.)
Transcribed Image Text:A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 105, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about µ if the sample size, n, is 16. μ (b) Construct a 98% confidence interval about µ if the sample size, n, is 26. (c) Construct a 99% confidence interval about u if the sample size, n, is 16. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Click the icon to view the table of areas under the t-distribution. (a) Construct a 98% confidence interval about µ if the sample size, n, is 16. μ Lower bound: 98.5; Upper bound: 111.5 (Use ascending order. Round to one decimal place as needed.) (b) Construct a 98% confidence interval about µ if the sample size, n, is 26. Lower bound: 100.1 ; Upper bound: 109.9 (Use ascending order. Round to one decimal place as needed.) How does increasing the sample size affect the margin of error, E? A. As the sample size increases, the margin of error stays the same. B. As the sample size increases, the margin of error decreases. C. As the sample size increases, the margin of error increases. (c) Construct a 99% confidence interval about µ if the sample size, n, is 16. Lower bound:; Upper bound: (Use ascending order. Round to one decimal place as needed.)
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Cn you make your answer more clearer cant see the writing 

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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 105, and the sample standard deviation, \( s \), is found to be 10. (a) Construct a 98% confidence interval about \(\mu\) if the sample size, \( n \), is 16. **Lower bound:** 98.5 ; **Upper bound:** 111.5 (Use ascending order. Round to one decimal place as needed.) (b) Construct a 98% confidence interval about \(\mu\) if the sample size, \( n \), is 26. **Lower bound:** 100.1 ; **Upper bound:** 109.9 (Use ascending order. Round to one decimal place as needed.) (c) Construct a 99% confidence interval about \(\mu\) if the sample size, \( n \), is 16. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? *Click the icon to view the table of areas under the t-distribution.* --- **How does increasing the sample size affect the margin of error, \( E \)?** *** - **A.** As the sample size increases, the margin of error stays the same. - **B.** As the sample size increases, the margin of error decreases. - **C.** As the sample size increases, the margin of error increases.
Transcribed Image Text: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 105, and the sample standard deviation, \( s \), is found to be 10. (a) Construct a 98% confidence interval about \(\mu\) if the sample size, \( n \), is 16. **Lower bound:** 98.5 ; **Upper bound:** 111.5 (Use ascending order. Round to one decimal place as needed.) (b) Construct a 98% confidence interval about \(\mu\) if the sample size, \( n \), is 26. **Lower bound:** 100.1 ; **Upper bound:** 109.9 (Use ascending order. Round to one decimal place as needed.) (c) Construct a 99% confidence interval about \(\mu\) if the sample size, \( n \), is 16. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? *Click the icon to view the table of areas under the t-distribution.* --- **How does increasing the sample size affect the margin of error, \( E \)?** *** - **A.** As the sample size increases, the margin of error stays the same. - **B.** As the sample size increases, the margin of error decreases. - **C.** As the sample size increases, the margin of error increases.
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Answer question (d) . 

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