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3. Pencil lead is a ceramic material consisting of clay and graphite; the clay provides the ceramic matrix supporting the graphite. Pencil lead formulation focuses on the ratio of clay to graphite: the more the clay, the firmer the grade and the lighter the mark made by the pencil. One measure of the ratio of clay to graphite is the "ash" content. Inspectors take a random sample of n = 40 pencils from a production process, extract the lead, and burn off all the "volatiles" (essentially the carbon) leaving the ash. The ash content, denoted by Y, is then weighed and reported as a percentage. A high ash content indicates too much clay in the formulation; a low ash content indicates too much graphite. The data are below. It is believed that 41.1 42.8 43.2 40.8 41.4 42.7 44.9 41.6 43.5 41.8 45.0 39.6 42.6 43.4 43.3 42.7 44.0 44.1 41.7 42.2 42.8 43.3 42.4 41.7 40.1 41.1 41.7 43.3 43.1 42.9 42.1 42.3 44.2 42.2 40.7 41.8 41.8 44.2 42.2 42.7 the mean ash content is differed from 42.5 percent. At the a = level, formulate a hypothesis test to investigate this assertion. . 0.1 significance

3. Pencil lead is a ceramic material consisting of clay and graphite; the clay provides the ceramic matrix supporting the graphite. Pencil lead formulation focuses on the ratio of clay to graphite: the more the clay, the firmer the grade and the lighter the mark made by the pencil. One measure of the ratio of clay to graphite is the "ash" content. Inspectors take a random sample of n = 40 pencils from a production process, extract the lead, and burn off all the "volatiles" (essentially the carbon) leaving the ash. The ash content, denoted by Y, is then weighed and reported as a percentage. A high ash content indicates too much clay in the formulation; a low ash content indicates too much graphite. The data are below. It is believed that 41.1 42.8 43.2 40.8 41.4 42.7 44.9 41.6 43.5 41.8 45.0 39.6 42.6 43.4 43.3 42.7 44.0 44.1 41.7 42.2 42.8 43.3 42.4 41.7 40.1 41.1 41.7 43.3 43.1 42.9 42.1 42.3 44.2 42.2 40.7 41.8 41.8 44.2 42.2 42.7 the mean ash content is differed from 42.5 percent. At the a = level, formulate a hypothesis test to investigate this assertion. . 0.1 significance

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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Please see attached to answer the following.

a. Calculate a 95% confidence interval for the population mean µ and interpret your interval in the context of this problem.

b. Could we have used the 95% confidence interval calculated in (a) to make a decision about the hypothesis test conducted? Explain why or why not. 

c. Engineers would like to engage in a larger study (where new pencils would be sampled) to estimate p = proportion of pencils with ash content greater than 42.5 percent. The goal is to write a 95% percent confidence interval for p whose total length is no greater than 0.06. How many observations should the engineers collect in their study?

3. Pencil lead is a ceramic material consisting of clay and graphite; the clay provides the ceramic matrix supporting the graphite. Pencil lead formulation focuses on the ratio of clay to graphite: the more the clay, the firmer the grade and the lighter the mark made by the pencil. One measure of the ratio of clay to graphite is the "ash" content. Inspectors take a random sample of n = 40 pencils from a production process, extract the lead, and burn off all the "volatiles" (essentially the carbon) leaving the ash. The ash content, denoted by Y, is then weighed and reported as a percentage. A high ash content indicates too much clay in the formulation; a low ash content indicates too much graphite. The data are below. It is believed that 41.1 42.8 43.2 40.8 41.4 42.7 44.9 41.6 43.5 41.8 45.0 39.6 42.6 43.4 43.3 42.7 44.0 44.1 41.7 42.2 42.8 43.3 42.4 41.7 40.1 41.1 41.7 43.3 43.1 42.9 42.1 42.3 44.2 42.2 40.7 41.8 41.8 44.2 42.2 42.7 the mean ash content is differed from 42.5 percent. At the a = level, formulate a hypothesis test to investigate this assertion. . 0.1 significance
Transcribed Image Text:3. Pencil lead is a ceramic material consisting of clay and graphite; the clay provides the ceramic matrix supporting the graphite. Pencil lead formulation focuses on the ratio of clay to graphite: the more the clay, the firmer the grade and the lighter the mark made by the pencil. One measure of the ratio of clay to graphite is the "ash" content. Inspectors take a random sample of n = 40 pencils from a production process, extract the lead, and burn off all the "volatiles" (essentially the carbon) leaving the ash. The ash content, denoted by Y, is then weighed and reported as a percentage. A high ash content indicates too much clay in the formulation; a low ash content indicates too much graphite. The data are below. It is believed that 41.1 42.8 43.2 40.8 41.4 42.7 44.9 41.6 43.5 41.8 45.0 39.6 42.6 43.4 43.3 42.7 44.0 44.1 41.7 42.2 42.8 43.3 42.4 41.7 40.1 41.1 41.7 43.3 43.1 42.9 42.1 42.3 44.2 42.2 40.7 41.8 41.8 44.2 42.2 42.7 the mean ash content is differed from 42.5 percent. At the a = level, formulate a hypothesis test to investigate this assertion. . 0.1 significance
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