**Problem 1 - Setup:**D.C. Montgomery discusses a case in which the tensile strength of a synthetic fiber used to make cloth for men's shirts is of interest to a manufacturer. It is suspected that the strength is affected by the percentage of cotton in the fiber. Three levels of cotton percentage are considered, and five observations are taken at each level. The 15 experiments are run in random order.This dataset (Cotton.xlsx) is available on Blackboard. There is a header. Note that in order for cotton to be considered as a factor in R, it cannot just consist of numeric values, so the cotton percentages are listed as C20, C25, C35, instead of 20, 25, 35. The dataset is shown below.| % Cotton | pounds per square inch | \( \bar{Y_i} \) | \( \sum Y_{ij} \) | \( \sum Y_{ij}^2 \) | \( s_i^2 \) ||----------|------------------------|-----------------|-------------------|--------------------|------------|| 20 | 12 17 17 18 18 | 15.4 | 77 | 1225 | 9.8 || 25 | 13 18 18 19 19 | 17.4 | 87 | 1539 | 6.3 || 35 | 7 10 11 15 11 | 10.8 | 54 | 616 | 8.2 |If the cotton percentages are three levels randomly selected from a big set of cotton percentages, i.e., a model with a random factor should be considered for analysis.1. **Write down appropriate statistical models for the analysis with necessary assumptions.**2. **Complete the ANOVA Table:** | Source | SS | df | MS | F | |--------------|--------|----|-----|----| | % Cotton (Trt) | 114.53 | | | | | Error | 97.20 | | | | | Total | 211.73 | | | |3. **State the null and alternative hypotheses. Perform a hypothesis test and calculate its p-value. Use a 0.05 significance level

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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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