Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Textbook Question
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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A. based on the sample data, does the treatment, does the treatment have a significant effect? Test with a=.01. ( make sure you have ALL the steps involved in a hypothesis test).
B. Calculate Cohens d to estimate the effect size.
C. What a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear on a research report.
Josh wants to convince his mother to stop buying single-ply toilet paper. Josh believes that even though Fluffy, a two-ply toilet paper costs more, it will last longer because it is more absorbent. To help substantiate his claim, Josh performed a study. He purchased a random sample of 18 rolls of Fluffy. For each roll, he determined how many squares are needed to completely absorb one-quarter cup of water. Here is a dotplot of the data.
The mean of the sample is 24.444 squares with a standard deviation of 2.45 squares. Single-ply toilet paper requires 26 squares to absorb one-quarter cup of water. Josh would like to carry out a test to determine if there is convincing evidence that the mean number of squares of Fluffy that are needed to absorb one-quarter cup of water is fewer than 26 squares. What is the appropriate test statistic and P-value of this test?
(A) z = -2.69z=−2.69, PP-value = 0.0036=0.0036
(B) t = -2.69t=−2.69, PP-value = 0.0078=0.0078
(C) t = -2.69t=−2.69, PP-value =…
At a research facility that designs rocket engines, researchers know that some engines fail to ignite as a result of fuel system error. From a random sample of 40 engines of one design, 14 failed to ignite as a result of fuel system error. From a random sample of 30 engines of a second design, 9 failed to ignite as a result of fuel system error. The researchers want to estimate the difference in the proportion of engine failures for the two designs. Which of the following is the most appropriate method to create the estimate?
A one-sample zz-interval for a sample proportion
A
A one-sample zz-interval for a population proportion
B
A two-sample zz-interval for a population proportion
C
A two-sample zz-interval for a difference in sample proportions
D
A two-sample zz-interval for a difference in population proportions
Chapter 9 Solutions
Statistics for Engineers and Scientists
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