Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Chapter 9.3, Problem 1E
To assess the effect of piston ring type and oil type on piston ring wear, three types of piston ring and four types of oil were studied. Three replications of an experiment, in which the number of milligrams of material lost from the ring in four hours of running was measured, were carried out for each of the 12 combinations of oil type and piston ring type. With oil type as the row effect and piston ring type as the column effect, the following sums of squares were observed: SSA = 1.0926, SSB = 0.9340, SSAB = 0.2485, SSE = 1.7034.
- a. How many degrees of freedom are there for the effect of oil type?
- b. How many degrees of freedom are there for the effect of piston ring type?
- 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 oil type 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 piston ring type are all equal to 0? Provide the value of the test statistic and the P-value.
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To assess the effect of piston ring type and oil type on piston ring wear, three types of piston ring and four types of oil were studied. Three replications of an experiment, in which the number of milligrams of material lost from the ring in four hours of running was measured, were carried out for each of the 12 combinations of oil type and piston ring type. With oil type as the row effect and piston ring type as the column effect, the following sums of squares were observed: SSA = 1.0926, SSB = 0.9340, SSAB = 0.2485, SSE = 1.7034. a) How many degrees of freedom are there for the effect of oil type? b) How many degrees of freedom are there for the effect of piston ring type? 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…
In a study of a group of women science majors who remained in their profession and a group who left their profession within a few months of graduation, the researchers collected the data shown here on a self-esteem questionnaire.
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1 = 3.09
2 = 2.92
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Chapter 9 Solutions
Statistics for Engineers and Scientists
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