A machine shop has three machines used in precision grinding of cam rollers. Three machinists are employed to grind rollers on the machines. In an experiment to determine whether there are differences in output among the machines or their operators, each operator worked on each machine on four different days. The outcome measured was the daily production of parts that met specifications. With the operator as the row effect and the machine as the column effect, the following sums of squares were observed: SSA = 3147.0, SSB = 136.5, SSAB = 411.7, SSE = 1522.0.
- a. How many degrees of freedom are there for the operator effect?
- b. How many degrees of freedom are there for the machine effect?
- c. How many degrees of freedom are there for interactions?
- d. How many degrees of freedom are there for error?
- e. Construct an ANOVA table. You may give
ranges for the P-values. - f. Is the additive model plausible? Provide the value of the test statistic and the P-value.
- g. Is it plausible that the main effects of operator are all equal to 0? Provide the value of the test statistic and the P-value.
- h. Is it plausible that the main effects of machine are all equal to 0? Provide the value of the test statistic and the P-value.
Trending nowThis is a popular solution!
Chapter 9 Solutions
Statistics for Engineers and Scientists
Additional Math Textbook Solutions
Essentials of Statistics, Books a la Carte Edition (5th Edition)
Statistics Through Applications
Introduction to Statistical Quality Control
Elementary Statistics (Text Only)
- Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. (d) In a month of 200 flight journeys finished, how many should have arrived 5 minutes or less earlier?arrow_forwardA man has just purchased a trick die which was advertised as not yielding the proper proportion of sixes. He wonders whether the advertising was correct, and tests the advertising claim by rolling the die 100 times. The 100 rolls yielding 10 sixes. Should he conclude that the advertising was legitimate?arrow_forwardAt the end of summer, the total weight of seeds accumulated by a nest of seed-gathering ants will vary from nest to nest. If the expected total weight of seeds gathered by a randomly chosen nest is 5 pounds, and the standarddeviationis0.5pounds,whatistheprobabilitythatthetotalcombinedweightoftheseedsgatheredby100 nests will be larger than 495 pounds by the end of next summer? To answer this question most accurately, given the information available, we would use: 1. Chebyshev’s theorem 2.Markov’s theorem (3.The Central Limit Theorem 4.The joint probability that the weight of seeds is larger than 5 pounds in each nest.arrow_forward
- For a particular population, a sample of n = 4 scores has a standard error of 6. For the same population, a sample of n = 16 scores would have a standard error of _____arrow_forwarda major cereal manufacturer is awarding prize certificates in its #1 cereal. a random sample of 60 cereal boxes is selected and 5 are found to contain prize certificates. find the 90% C.I for the true proportion of prize certificates.arrow_forwardIn a public opinion survey, 60 out of a sample of 100 high-income voters and 40 out of a sample of 75 low-income voters supported a decrease in value-added tax, VAT. Conclude at the 5% level of significance that the population of voters favouring a VAT decrease differs between high- and low-income voters. (Where p1 is the proportion of all high-income voters who supported a decrease in VAT; p2 is the same for the low-income voters). The rejection region to test the above hypothesis at the 5% significance level (rounded off to two decimals) is: A. T < -1.96 B. T < -1.64 or Z > 1.64 C. Z < -1.96 or Z > 1.96 D. Z < -1.64 E. None of the precedingarrow_forward
- In a public opinion survey, 60 out of a sample of 100 high-income voters and 40 out of a sample of 75 low-income voters supported a decrease in value-added tax, VAT. Conclude at the 5% level of significance that the population of voters favouring a VAT decrease differs between high- and low-income voters. (Where p1 is the proportion of all high-income voters who supported a decrease in VAT; p2 is the same for the low-income voters). The rejection region to test the above hypothesis at the 5% significance level is: A. T < - 1.96 B. T < - 1.96 or Z > 1.64 C. Z< - 1.96 or Z > 1.96 D. Z < -1.64arrow_forwarda) which for these data is 32.1470, 42.3520, or 10.0674 c) that minimizes the error sum of squares, total sum of squares, or regression sum of squares…for which these data is 32.1470, 42.3520, or 10.0674arrow_forwarda) by the…regression sum of squares, error sum of squares, or total sum of squares…which for these data is…318.8361, 41.9197, or 362.0680 c) minimizes the…regression sum of squares, error sum of squares, or total sum of squares…which for these data is…318.8361, 41.9197, or 362.0680arrow_forward
- In a study of the causes of bearing wear, a machine was run 24 times, with various loads (denoted x1), oil viscosities (x2), and ambient temperatures (x3). The wear, denoted y, was modeled as y = β0 + β1x1 + β2x2 + β3x3 + ε. When this model was fit to the data, the sum of squares for error was SSE = 9.37. Then the reduced model y = β0 + β1x1 + β2x2 + β3x3 was fit, and the sum of squares for error was SSE = 27.49. Is it reasonable to use the reduced model, rather than the model containing all the interactions, to predict wear? Explain.arrow_forwardConsider a study in which the sum of squares (SS) based on an experimental group of 10 participants is 100, and the SS based on a control group of 20 participants is 250. The estimated starboard error of this study is ___.arrow_forwardA city official claims that the proportion of all commuters who are in favor of an expanded public transportation system is 50%. A newspaper conducts a survey to determine whether this proportion is different from 50%. Out of 225 randomly chosen commuters, the survey finds that 99 of them reply yes when asked if they support an expanded public transportation system. Test the official’s claim at α= 0.05.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage