### Determining Sample Size for Confidence Interval Estimation#### Problem StatementHow heavy a load, in pounds, is needed to pull apart pieces of Douglas fir 4 in. long and 1.5 in. wide with a standard deviation \( \sigma \) of 3000 lbs? Estimate the mean load \( \mu \) needed to pull apart the pieces of wood to within plus or minus 600 lbs with 95% confidence.**Objective:**Determine how large of a sample size \( n \) is needed.---This problem involves statistics, specifically estimating the sample size needed for a confidence interval on a mean. The challenge is to find the appropriate sample size \( n \) that allows us to estimate the mean load \( \mu \) within a margin of error (E) of ±600 lbs, at a 95% confidence level, given the standard deviation \( \sigma \).#### Solution Steps:1. **Identify the Known Parameters:** - \( \sigma \) (Standard Deviation): 3000 lbs - Margin of Error \( E \): 600 lbs - Confidence Level: 95%2. **Identify the Z-value Corresponding to the 95% Confidence Level:** - At 95% confidence, the Z-value (z*) is approximately 1.96.3. **Use the Margin of Error Formula for the Mean:** \[ E = z^* \frac{\sigma}{\sqrt{n}} \]4. **Rearrange the Formula to Solve for Sample Size \( n \):** \[ \sqrt{n} = \frac{z^* \sigma}{E} \] \[ n = \left( \frac{z^* \sigma}{E} \right)^2 \]5. **Plug in the Values and Calculate \( n \):** \[ n = \left( \frac{1.96 \times 3000}{600} \right)^2 \] \[ n = \left( \frac{5880}{600} \right)^2 \] \[ n = 9.8^2 \] \[ n \approx 96.04 \]6. **Round Up to Ensure Adequate Sample Size:** \[

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How heavy a load, in pounds, is needed to pull apart pieces of Douglas fir 4 in. long and 1.5 in. wide with a standard deviation o of 3000 lbs? Estimate the mean load needed to pull apart the pieces of wood to within plus or minus 600 lbs with 95% confidence. Determine how large of a sample size n is needed.

How heavy a load, in pounds, is needed to pull apart pieces of Douglas fir 4 in. long and 1.5 in. wide with a standard deviation o of 3000 lbs? Estimate the mean load needed to pull apart the pieces of wood to within plus or minus 600 lbs with 95% confidence. Determine how large of a sample size n is needed.

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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