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The mean and standard deviation of a random sample of n measurements are equal to 33.1 and 3.6, respectively. a. Find a 95% confidence interval for u if n = 100. b. Find a 95% confidence interval for μ if n = 400. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed? a. The 95% confidence interval for μ if n = 100 is approximately (Round to three decimal places as needed.) b. The 95% confidence interval μ if n = 400 is approximately - (Round to three decimal places as needed.) C... c. Choose the correct answer below. OA. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4. OB. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 4. OC. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval. OD. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2. OE. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.

The mean and standard deviation of a random sample of n measurements are equal to 33.1 and 3.6, respectively. a. Find a 95% confidence interval for u if n = 100. b. Find a 95% confidence interval for μ if n = 400. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed? a. The 95% confidence interval for μ if n = 100 is approximately (Round to three decimal places as needed.) b. The 95% confidence interval μ if n = 400 is approximately - (Round to three decimal places as needed.) C... c. Choose the correct answer below. OA. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4. OB. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 4. OC. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval. OD. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2. OE. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.

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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The mean and standard deviation of a random sample of n measurements are equal to 33.1 and 3.6, respectively. a. Find a 95% confidence interval for u if n = 100. b. Find a 95% confidence interval for u if n 400. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed? a. The 95% confidence interval for μ if n = 100 is approximately (). (Round to three decimal places as needed.) b. The 95% confidence interval μ if n = 400 is approximately ( (Round to three decimal places as needed.) c. Choose the correct answer below. O A. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4. O B. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 4. OC. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval. O D. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2. O E. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
Transcribed Image Text:The mean and standard deviation of a random sample of n measurements are equal to 33.1 and 3.6, respectively. a. Find a 95% confidence interval for u if n = 100. b. Find a 95% confidence interval for u if n 400. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed? a. The 95% confidence interval for μ if n = 100 is approximately (). (Round to three decimal places as needed.) b. The 95% confidence interval μ if n = 400 is approximately ( (Round to three decimal places as needed.) c. Choose the correct answer below. O A. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4. O B. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 4. OC. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval. O D. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2. O E. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
Expert Solution
Step 1: Determine the given information

For a random sample of n observations, it is obtained that:

The sample mean, x¯=33.1

And the sample standard deviation, s=3.6

The objective is to obtain the confidence interval for μ (population mean) with the desired confidence of 95%.

As the population variance, σ2 is unknown, the t-critical value is to be considered.




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