### Confidence Interval CalculationsA random sample of 92 observations produced a mean (x̄) of 25.8 and a standard deviation (s) of 2.4.#### Tasks:a. Find a 95% confidence interval for μ. b. Find a 90% confidence interval for μ. c. Find a 99% confidence interval for μ. ### Step-by-Step Solution:**1. Identify the parameters:**- Sample mean (x̄) = 25.8- Sample standard deviation (s) = 2.4- Sample size (n) = 92**2. Calculate the standard error of the mean (SEM):**\[ \text{SEM} = \frac{s}{\sqrt{n}} = \frac{2.4}{\sqrt{92}} \]**3. Use the appropriate z-score for each confidence level:**- For a 95% confidence interval, the z-score is approximately 1.96.- For a 90% confidence interval, the z-score is approximately 1.645.- For a 99% confidence interval, the z-score is approximately 2.576.**4. Calculate the margin of error (ME):**\[ \text{ME} = z \times \text{SEM} \]**5. Construct the confidence intervals:**\[ \text{Confidence Interval} = x̄ \pm \text{ME} \]**a. 95% Confidence Interval:**- Calculate SEM:\[ \text{SEM} = \frac{2.4}{\sqrt{92}} \approx 0.25 \]- Calculate ME:\[ \text{ME} = 1.96 \times 0.25 \approx 0.49 \]- Confidence Interval:\[ 25.8 \pm 0.49 = (25.31, 26.29) \]**b. 90% Confidence Interval:**- Calculate ME:\[ \text{ME} = 1.645 \times 0.25 \approx 0.41 \]- Confidence Interval:\[ 25.8 \pm 0.41 = (25.39, 26.21) \]**c. 99% Confidence Interval:**- Calculate ME:\[ \text{ME} = 2.576 \times 0

Introduction: As the population standard deviation is unknown and the sample standard deviation is…

A random sample of 92 observations produced a mean x = 25.8 and a standard deviation s = 2.4. a. Find a 95% confidence interval for µ. b. Find a 90% confidence interval for µ. c. Find a 99% confidence interval for u.

A random sample of 92 observations produced a mean x = 25.8 and a standard deviation s = 2.4. a. Find a 95% confidence interval for µ. b. Find a 90% confidence interval for µ. c. Find a 99% confidence interval for u.

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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