### Estimating the Mean Height of 9th Grade StudentsTo estimate the mean height of all 9th grade students at one high school, consider the following information and calculations.**Given Data:**- Population standard deviation (σ): 5 inches- Heights of 9 randomly selected students (in inches): 70, 69, 63, 73, 67, 65, 70, 63, 73**Sample Mean (\(\bar{x}\)):**The sample mean height is calculated by taking the average of the heights of the 9 students.\[ \bar{x} = \frac{(70 + 69 + 63 + 73 + 67 + 65 + 70 + 63 + 73)}{9} \approx 68.11 \text{ inches} \]**Margin of Error at 95% Confidence Level:**The margin of error (E) can be calculated using the formula for the confidence interval for a mean:\[ E = z \left(\frac{\sigma}{\sqrt{n}}\right) \]Where:- \( z \) is the z-value corresponding to the 95% confidence level (approximately 1.96).- \( \sigma \) is the population standard deviation (5 inches).- \( n \) is the sample size (9).\[ E = 1.96 \left(\frac{5}{\sqrt{9}}\right) = 1.96 \times \frac{5}{3} \approx 3.27 \text{ inches} \]**95% Confidence Interval:**The 95% confidence interval for the population mean is calculated as:\[ CI = \left[ \bar{x} - E, \bar{x} + E \right] \]Substituting the values:\[ CI \approx \left[ 68.11 - 3.27, 68.11 + 3.27 \right] \]\[ CI \approx \left[ 64.84, 71.38 \right] \]**Summary:**- Sample Mean (\(\bar{x}\)): ~68.11 inches- Margin of Error (E) at 95% confidence level: ~3.27 inches- 95% Confidence Interval: [64.84 inches, 71.38 inches]This interval suggests that we are 95% confident that

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Suppose the mean height in inches of all 9th grade students at one high school is estimated. The population standard deviation is 5 inches. The heights of 9 randomly selected students are 70, 69, 63, 73, 67, 65, 70, 63 and 73. Ex: 12.34 %3D Margin of error at 95% confidence level = Ex: 1.23 95% confidence interval = [ Ex: 12.34 Ex: 12.34 ] [smaller value, larger value]

Suppose the mean height in inches of all 9th grade students at one high school is estimated. The population standard deviation is 5 inches. The heights of 9 randomly selected students are 70, 69, 63, 73, 67, 65, 70, 63 and 73. Ex: 12.34 %3D Margin of error at 95% confidence level = Ex: 1.23 95% confidence interval = [ Ex: 12.34 Ex: 12.34 ] [smaller value, larger value]

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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