The accompanying data resulted from an experiment to investigate whether yield from a certain chemical process depended either on the formulation of a particular input or on mixer speed. A statistical computer package gave SS(Form) = 2253.44, SS(Speed) = 230.81, SS(Form*Speed) = 18.58, and SSE = 71.87. a. Does there appear to be interaction between the factors? b. Does yield appear to depend on either formulation or speed? c. Calculate estimates of the main effects. d. The fitted values are x ^ i j k = μ ^ + α ^ i + β ^ j + γ ^ i j , and the residuals are x i j k − x ^ i j k . Verify that the residuals are .23, −.87, .63, 4.50, −1.20, −3.30, −2.03, 1.97,.07, −1.10, −.30, 1.40, .67, −1.23, .57, −3.43, −.13,and 3.57. e. Construct a normal probability plot from the residuals given in part (d). Do the ϵ ijk ’s appear to be normally distributed?

BuyFind

Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809
BuyFind

Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809

Solutions

Chapter 11.2, Problem 18E
Textbook Problem

The accompanying data resulted from an experiment to investigate whether yield from a certain chemical process depended either on the formulation of a particular input or on mixer speed.

Chapter 11.2, Problem 18E, The accompanying data resulted from an experiment to investigate whether yield from a certain

A statistical computer package gave SS(Form) = 2253.44, SS(Speed) = 230.81, SS(Form*Speed) = 18.58, and SSE = 71.87.

a. Does there appear to be interaction between the factors?

b. Does yield appear to depend on either formulation or speed?

c. Calculate estimates of the main effects.

d. The fitted values are x ^ i j k = μ ^ + α ^ i + β ^ j + γ ^ i j , and the residuals are x i j k x ^ i j k . Verify that the residuals are .23, −.87, .63, 4.50, −1.20, −3.30, −2.03, 1.97,.07, −1.10, −.30, 1.40, .67, −1.23, .57, −3.43, −.13,and 3.57.

e. Construct a normal probability plot from the residuals given in part (d). Do the ϵijk’s appear to be normally distributed?

Expert Solution

Want to see the full answer?

Check out a sample textbook solution.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects.

Chapter 11 Solutions

Probability and Statistics for Engineering and the Sciences
Ch. 11.1 - For the data of Example 11.5, check the...Ch. 11.1 - Suppose that in the experiment described in...Ch. 11.1 - a. Show that a constant d can be added to (or...Ch. 11.1 - Use the fact that E(Xij) = + i + j with i=j=0 to...Ch. 11.1 - The power curves of Figures 10.5 and 10.6 can be...Ch. 11.2 - In an experiment to assess the effects of curing...Ch. 11.2 - The article Towards Improving the Properties of...Ch. 11.2 - The accompanying data resulted from an experiment...Ch. 11.2 - A two-way ANOVA was carried out to assess the...Ch. 11.2 - The article Fatigue Limits of Enamel Bonds with...Ch. 11.2 - In an experiment to investigate the effect of...Ch. 11.2 - A study was carried out to compare the writing...Ch. 11.2 - The accompanying data was obtained in an...Ch. 11.2 - a. Show that E(Xi..X)=i, so that Xi..X is an...Ch. 11.2 - Show how a 100(1 )% t CI for i i, can be...Ch. 11.2 - When both factors are random in a two-way ANOVA...Ch. 11.3 - The output of a continuous extruding machine that...Ch. 11.3 - To see whether thrust force in drilling is...Ch. 11.3 - The article Effects of Household Fabric Softeners...Ch. 11.3 - The following summary quantities were computed...Ch. 11.3 - Nickel titanium (NiTi) shape memory alloy (SMA)...Ch. 11.3 - When factors A and B are fixed but factor C is...Ch. 11.3 - Because of potential variability in aging due to...Ch. 11.3 - The article The Responsiveness of Food Sales to...Ch. 11.3 - The article Variation in Moisture and Ascorbic...Ch. 11.3 - The article An Assessment of the Effects of...Ch. 11.3 - A four-factor ANOVA experiment was carried out to...Ch. 11.4 - The accompanying data resulted from an experiment...Ch. 11.4 - The accompanying data resulted from a 23...Ch. 11.4 - In a study of processes used to remove impurities...Ch. 11.4 - As with many dried products, sun-dried tomatoes...Ch. 11.4 - The following data on power consumption in...Ch. 11.4 - The article Statistical Design and Analysis of...Ch. 11.4 - a. In a 24 experiment, suppose two blocks are to...Ch. 11.4 - a. An experiment was carried out to investigate...Ch. 11.4 - In an experiment involving four factors (A, B, C,...Ch. 11.4 - a. In a seven-factor experiment (A,, G), suppose a...Ch. 11.4 - The article Applying Design of Experiments to...Ch. 11 - The results of a study on the effectiveness of...Ch. 11 - The water absorption of two types of mortar used...Ch. 11 - Four plots were available for an experiment to...Ch. 11 - In an automated chemical coating process, the...Ch. 11 - Coal-fired power plants used in the electrical...Ch. 11 - Impurities in the form of iron oxides lower the...Ch. 11 - Factorial designs have been used in forestry to...Ch. 11 - One property of automobile air bags that...Ch. 11 - A chemical engineer has carried out an experiment...Ch. 11 - The bond strength when mounting an integrated...Ch. 11 - The article Effect of Cutting Conditions on Tool...Ch. 11 - Analogous to a Latin square, a Greco-Latin square...

Additional Math Textbook Solutions

Find more solutions based on key concepts
Describe three ways that a risk-averse person might reduce the risk she faces.

Brief Principles of Macroeconomics (MindTap Course List)

What is a loan amortization schedule, and what are some ways these schedules are used?

Fundamentals of Financial Management, Concise Edition (MindTap Course List)

What is behavior modification and how is it used in organizations?

Foundations of Business (MindTap Course List)

Planning a Grand Tour A grand tour of four cities begins at City A and makes successive stops at cities B, C, a...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Solve the equations in Exercises 126. (x+1)3+(x+1)5=0

Finite Mathematics and Applied Calculus (MindTap Course List)

Finding a Derivative In Exercises 57-82, find the derivative of the function. g(x)=lnx

Calculus: Early Transcendental Functions (MindTap Course List)

(i · j)k = k 2-k 0 (the number 0) 0 (the zero vector)

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: is a rational function.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Daily Patient Volume at Dental Clinic. A sample of 9 days over the past six months showed that Philip Sherman, ...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

5.1.1Spring/Mass Systems: Free Undamped Motion A mass weighing 10 pounds stretches a spring 14 foot. This mass ...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

ReminderRound all answers to two decimal places unless otherwise indicated. Sketching a Graph with Given Concav...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)