### 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:** \[

Answered: Image /qna-images/answer/8464e8c3-9c46-49a8-99ee-18d6895b6c0e.jpg

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

See similar textbooks

Similar questions

A variable of a population has a mean of u = 83 and a standard deviation of o = 24. a. Identify the sampling distribution of the sample mean for samples of size 36. b. In answering part (a), what assumptions did you make about the distribution of the variable? c. Can you answer part (a) if the sample size is 25 instead of 36? Why or why not? a. What is the shape of the sampling distribution? normal bimodal uniform skewed What is the mean of the sampling distribution? H = (Simplify your answer.)
A grocer finds that the cantaloupes in his store have weights with mean 0.7 kg and standard deviation 53 grams. If this is true, then 99.7% of cantaloupes will have weights between how many grams?
A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected, and the diamęter is measured. The resulting data (in millimeters) are as follows: 8.24, 8.25, 8.20, 8.23, 8.24, 8.21, 8.26, 8.26, 8.20, 8.25, 8.23, 8.23 , 8.19, 8.27, 8.24. A conclusion has to be made at 1% significance that the mean rod diameter is greater than 8.20. What is the value of teale? Please report your answer in 3 decimal places.
Assume we know the following for a paired-samples t test: N = 32, Mdifference = 1.75, s = 4
may i know the answer??????????
Engineers want to design seats in commercial aircraft so that they are wide enough to fit 95% of all males. (Accommodating 100% of males would require very wide seats that would be much to0 expensive.) Men have hip breadths that are normally distributed with a mean of 14.7 in. and a standard deviation of 0.9 in. Find Por. That is, find the hip breadth for men that separates the smallest 95% from the largest 5%. The hip breadth for men that separates the smallest 95% from the largest 5% is Pas = (Round to one decimal place as needed.) in.
Assume that a sample is used to estimate a population proportion μμ. Find the margin of error M.E.that corresponds to a sample of size 84 with a mean of 79.2 and a standard deviation of 6.1 at a confidence level of 99.9%.Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
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 22 with a mean of 62.5 and a standard deviation of 9.6 at a confidence level of 80%.Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. =
The screws to be used on a building construction have an average length of 20 cm withStd Dev of 0.9 cm, following a Normal Distribution.The specifications for the minimum and maximum lengths are 17.5 cm and 23 cmrespectively. If a batch of 100,000 screws is received, how many would be acceptedbecause they are inside the specifications?
Given a normal distribution with mean 25 and standard deviation 5, find the area under the normal curve from the men to the indicated measurement. A) 36.1?
how many women must be randomly selected to estimate the mean weight of women in one age group. we want 90% confidence that the sample mean is within 3.4 lb of the population mean, andthe population standard deviation is known to be 25 lb. A) 147 B) 148 C) 208 D) 146