**Estimating the Margin of Error for a Population Mean**To estimate the population mean \(\mu\), begin with a sample. Let's find the margin of error \(M.E.\) for a sample of size 22, with a mean of 30.6 and a standard deviation of 7.9, at a 99% confidence level.### Steps to Calculate the Margin of Error1. **Determine the Sample Statistics:** - Sample size (n) = 22 - Sample mean (\(\overline{x}\)) = 30.6 - Sample standard deviation (s) = 7.92. **Identify the Confidence Level:** - Confidence level = 99%3. **Find the Critical Value:** - For a 99% confidence level, find the corresponding t-value from the t-distribution table. Use degrees of freedom (df) = \( n - 1 = 22 - 1 = 21 \).4. **Calculate the Margin of Error (M.E.):** - Formula: \( M.E. = t \times \frac{s}{\sqrt{n}} \) - Ensure that the margin of error is reported to one decimal place due to the accuracy of the sample statistics. - Conduct calculations without preliminary rounding, but the critical value may be rounded to three decimal places if necessary.### Please Enter the Calculated Margin of Error\[ M.E. = \boxed{} \]### Important Note:The answer should reflect accurate representation considering the specific context provided. The critical value and standard deviation must consider formatting and precision as specified.

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Answered: Assume that a sample is used to…

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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Assume that a sample is used to estimate a population mean μμ. Find the margin of error M.E. that corresponds to a sample of size 11 with a mean of 57.8 and a standard deviation of 7.7 at a confidence level of 98%.Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.M.E. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
Assume that a sample is used to estimate a population mean μ. Find the margin of error M.E. that corresponds to a sample of size 21 with a mean of 83.8 and a standard deviation of 18.9 at a confidence level of 99%.Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
If the standard deviation of hole diameter significantly exceeds 0.011 mm, there is an unacceptably high probability that a rivet designed to be placed in the hole will not fit. After drilling 30 of these holes, a sample standard deviation in hole diameter was calculated as 0.012 mm. Construct a 95% interval estimate for the true deviation of the hole diameters and discuss the likelihood of the standard deviation exceeding our target.
Assume that a sample is used to estimate a population mean μμ. Find the margin of error M.E. that corresponds to a sample of size 17 with a mean of 44.6 and a standard deviation of 10.1 at a confidence level of 99.8%.Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.M.E. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
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