2.99 See Answer

Question: A 22 factorial experiment is analyzed by

A 22 factorial experiment is analyzed by the Statistics Consulting Center at Virginia Tech. The client is a member of the Department of Housing, Interior Design, and Resource Management. The client is interested in comparing cold start to preheating ovens in terms of total energy delivered to the product. In addition, convection is being compared to regular mode. Four experimental runs are made at each of the four factor combinations. Following are the data from the experiment:
A 22 factorial experiment is analyzed by the Statistics Consulting Center at Virginia Tech. The client is a member of the Department of Housing, Interior Design, and Resource Management. The client is interested in comparing cold start to preheating ovens in terms of total energy delivered to the product. In addition, convection is being compared to regular mode. Four experimental runs are made at each of the four factor combinations. Following are the data from the experiment:


Do an analysis of variance to study main effects and interaction. Draw conclusions.

Do an analysis of variance to study main effects and interaction. Draw conclusions.





Transcribed Image Text:

Cold Convection 618 619.3 575 573.7 574 572 Preheat Mode 629 611 Regular 581 585.7 595 558 562 562 Mode 581 566


> In the study “The Use of Regression Analysis for Correcting Matrix Effects in the X-Ray Fluorescence Analysis of Pyrotechnic Compositions,” published in the Proceedings of the Tenth Conference on the Design of Experime

> Use the data from Exercise 13.14 on page 530 to see if the median amount of nitrogen lost in perspiration is different for the three levels of dietary protein. Exercise 13.14: The study Loss of Nitrogen Through Sweat by Preadolescent Boys Consuming Thre

> In Review Exercise 13.45 on page 555, use the Kruskal-Wallis test, at the 0.05 level of significance, to determine if the chemical analyses performed by the four laboratories give, on average, the same results. Exercise 13.45: Four laboratories are bein

> Service calls come to a maintenance center according to a Poisson process with λ calls per minute. A data set of 20 one-minute periods yields an average of 1.8 calls. If the prior for λ follows an exponential distribution with mean 2, determine the poste

> A study by a chemical company compared the drainage properties of two different polymers. Ten different sludges were used, and both polymers were allowed to drain in each sludge. The free drainage was measured in mL/min. (a) Use the sign test at the 0.

> In the article called “Risky Assumptions” by Paul Slovic, Baruch Fischoff, and Sarah Lichtenstein, published in Psychology Today (June 1980), the risk of dying in the United States from 30 activities and technologies is ranked by members of the League of

> Two judges at a college homecoming parade rank eight floats in the following order: (a) Calculate the rank correlation coefficient. (b) Test the null hypothesis that ρ = 0 against the alternative that ρ > 0. Use α

> A consumer panel tests nine brands of microwave ovens for overall quality. The ranks assigned by the panel and the suggested retail prices are as follows: Is there a significant relationship between the quality and the price of a microwave oven? Use a

> With reference to the weights and chest sizes of infants in Exercise 11.47 on page 436, (a) calculate the rank correlation coefficient; (b) test the hypothesis, at the 0.025 level of significance, that ρ = 0 against the alternative that Ï

> Calculate the rank correlation coefficient for the daily rainfall and amount of particulate removed in Exercise 11.13 on page 400. Exercise 11.13: A study of the amount of rainfall and the quantity of air pollution removed produced the following data:

> With reference to the data of Exercise 11.1 on page 398, (a) calculate the rank correlation coefficient; (b) test the null hypothesis, at the 0.05 level of significance, that ρ = 0 against the alternative that ρ = 0. Compare your r

> The following table gives the recorded grades for 10 students on a midterm test and the final examination in a calculus course: (a) Calculate the rank correlation coefficient. (b) Test the null hypothesis that ρ = 0 against the alternative t

> What is the probability that at least 95% of a population will exceed the smallest value in a random sample of size n = 135?

> How large a sample is required to be 99% confident that at least 80% of the population will be less than the largest observation in the sample?

> Repeat Exercise 18.2 when 1 of the next 4 drinks overflows and the uniform prior distribution is π(p) = 10, 0.05 < p < 0.15. Exercise 18.2: Let us assume that the prior distribution for the proportion p of drinks from a vending machine that overflow is

> What is the probability that the range of a random sample of size 24 includes at least 90% of the population?

> For the situation of Review Exercise 17.8, suppose that additional data are collected as follows: Does the process appear to be in control? Explain. Exercise 17.8: Samples of size 50 are taken every hour from a process producing a certain type of item

> Samples of size 50 are taken every hour from a process producing a certain type of item that is considered either defective or not defective. Twenty samples are taken. (a) Construct a control chart for control of proportion defective. (b) Does the proces

> How large a sample is required to be 95% confident that at least 85% of the distribution of measurements is included between the sample extremes?

> Consider the situation of Example 17.2. The following data are taken on additional samples of size 5. Plot the &Acirc;&macr;X - and S-values on the &Acirc;&macr;X - and S-charts that were produced with the data in the preliminary sample. Does the process

> Consider an in-control process with mean μ = 25 and σ = 1.0. Suppose that subgroups of size 5 are used with control limits μ ± 3σ/ √ n, and centerline at μ. Suppose that a shift occurs in the mean, and the new mean is μ = 26.5. (a) What is the average nu

> Consider the data of Table 17.1. Suppose that additional samples of size 5 are taken and tensile strength recorded. The sampling produces the following results (in pounds per square inch). (a) Plot the data, using the &Acirc;&macr;X - and R-charts for

> For the situation of Review Exercise 17.2, give numerical estimates of the mean and standard deviation of the diameter for the part being manufactured in the process. Exercise 17.2: Consider the following data taken on subgroups of size 5. The data cont

> Suppose for Review Exercise 17.2 that the buyer has set specifications for the part. The specifications require that the diameter fall in the range covered by 2.40000 &Acirc;&plusmn; 0.0100 mm. What proportion of units produced by this process will not c

> Consider the following data taken on subgroups of size 5. The data contain 20 averages and ranges on the diameter (in millimeters) of an important component part of an engine. Display &Acirc;&macr;X- and R-charts. Does the process appear to be in control

> A cigarette manufacturer claims that the tar content of brand B cigarettes is lower than that of brand A cigarettes. To test this claim, the following determinations of tar content, in milligrams, were recorded: Use the rank-sum test with &Icirc;&plusm

> Rework Exercise 16.6 by using the signed-rank test. Exercise 16.6: Two types of instruments for measuring the amount of sulfur monoxide in the atmosphere are being compared in an air-pollution experiment. The following readings were recorded daily for a

> Rework Exercise 16.7 by using the signed-rank test. Exercise 16.7: The following figures give the systolic blood pressure of 16 joggers before and after an 8-kilometer run: Use the sign test at the 0.05 level of significance to test the null hypothesi

> The following are the numbers of prescriptions filled by two pharmacies over a 20-day period: Use the signed-rank test at the 0.01 level of significance to determine whether the two pharmacies, on average, fill the same number of prescriptions against

> Assuming that the measurements of Exercise 1.14 on page 30 were recorded successively from left to right as they were collected, use the runs test, with α = 0.05, to test the hypothesis that the data represent a random sequence. Exercise 1.14: A tire ma

> Rework Exercise 16.5 by using the signed-rank test. Exercise 16.5: It is claimed that a new diet will reduce a person&acirc;&#128;&#153;s weight by 4.5 kilograms, on average, in a period of 2 weeks. The weights of 10 women were recorded before and after

> A quality control effort is being undertaken for a process where large steel plates are manufactured and surface defects are of concern. The goal is to set up a quality control chart for the number of defects per plate. The data are given below. Set up t

> Consider X1,X2, . . . , Xn independent Poisson random variables with parameters &Icirc;&frac14;1, &Icirc;&frac14;2, . . . , &Icirc;&frac14;n. Use the properties of moment-generating functions to show that the random variable / is a Poisson random varia

> Analyze the data of Exercise 16.2 by using the signed-rank test. Exercise 16.2: The following data represent the number of hours of flight training received by 18 student pilots from a certain instructor prior to their first solo flight: Using binomia

> Analyze the data of Exercise 16.1 by using the signed-rank test. Exercise 16.1: The following data represent the time, in minutes, that a patient has to wait during 12 visits to a doctor&acirc;&#128;&#153;s office before being seen by the doctor: Use

> The following figures give the systolic blood pressure of 16 joggers before and after an 8-kilometer run: Use the sign test at the 0.05 level of significance to test the null hypothesis that jogging 8 kilometers increases the median systolic blood pres

> Two types of instruments for measuring the amount of sulfur monoxide in the atmosphere are being compared in an air-pollution experiment. The following readings were recorded daily for a period of 2 weeks: Using the normal approximation to the binomial

> It is claimed that a new diet will reduce a person&acirc;&#128;&#153;s weight by 4.5 kilograms, on average, in a period of 2 weeks. The weights of 10 women were recorded before and after a 2-week period during which they followed this diet, yielding the

> A paint supplier claims that a new additive will reduce the drying time of its acrylic paint. To test this claim, 12 panels of wood were painted, one-half of each panel with paint containing the regular additive and the other half with paint containing t

> A food inspector examined 16 jars of a certain brand of jam to determine the percent of foreign impurities. The following data were recorded: Using the normal approximation to the binomial distribution, perform a sign test at the 0.05 level of signific

> In an industrial production line, items are inspected periodically for defectives. The following is a sequence of defective items, D, and nondefective items, N, produced by this production line: D D N N N D N N D D N N N N N D D D N N D N N N N D N D Use

> The following data represent the number of hours of flight training received by 18 student pilots from a certain instructor prior to their first solo flight: Using binomial probabilities from Table A.1, perform a sign test at the 0.02 level of signific

> The weights of 5 people before they stopped smoking and 5 weeks after they stopped smoking, in kilograms, are as follows: Use the signed-rank test for paired observations to test the hypothesis, at the 0.05 level of significance, that giving up smoking

> The following data represent the time, in minutes, that a patient has to wait during 12 visits to a doctor&acirc;&#128;&#153;s office before being seen by the doctor: Use the sign test at the 0.05 level of significance to test the doctor&acirc;&#128;&#

> Consider Exercise 15.6. Use a +1 and &acirc;&#136;&#146;1 scaling for &acirc;&#128;&#156;high&acirc;&#128;&#157; and &acirc;&#128;&#156;low,&acirc;&#128;&#157; respectively, and do a multiple linear regression with the model Yi = &Icirc;&sup2;0 + &Icirc;

> Consider Exercise 15.3 once again. Three-factor interactions are often not significant, and even if they are, they are difficult to interpret. The interaction ABD appears to be important. To gain some sense of interpretation, show two AD interaction plot

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> Use the runs test to test, at level 0.01, whether there is a difference in the average operating time for the two calculators of Exercise 16.17 on page 670. Exercise 16.17: The following data represent the number of hours that two different types of sci

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> A Plackett-Burman design was used to study the rheological properties of high-molecular-weight copolymers. Two levels of each of six variables were fixed in the experiment. The viscosity of the polymer is the response. The data were analyzed by the Stati

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> Consider the following 23 factorial with control variables x1 and x2 and noise variable z. Can x1 and x2 be chosen at levels for which Var(y) is minimized? Explain why or why not.

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> Consider Exercise 15.27. Construct another 26−3 that is different from the design chosen in Exercise 15.27. Exercise 15.27: There are six factors and only eight design points can be used. Construct a 26−3 by beginning with a 23 and use D = AB, E = −AC,

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> In the study Durability of Rubber to Steel Adhesively Bonded Joints, conducted at the Department of Environmental Science and Mechanics and analyzed by the Statistics Consulting Center at Virginia Tech, an experimenter measured the number of breakdowns i

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> In an experiment conducted by the Mining Engineering Department at Virginia Tech to study a particular filtering system for coal, a coagulant was added to a solution in a tank containing coal and sludge, which was then placed in a recirculation system in

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> Suppose a second replicate of the experiment in Exercise 15.13 could be performed. (a) Would a second replication of the blocking scheme of Exercise 15.13 be the best choice? (b) If the answer to part (a) is no, give the layout for a better choice for t

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> An experiment is described in Myers, Montgomery, and Anderson-Cook (2009) in which optimum conditions are sought for storing bovine semen to obtain maximum survival. The variables are percent sodium citrate, percent glycerol, and equilibration time in ho

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2.99

See Answer