Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 11.3, Problem 36E
To determine
Perform ANOVA to test the significance at 1% level of significance.
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The article “Monte Carlo Simulation—Tool for Better Understanding of LRFD” (J. of Structural Engr., 1993: 1586–1599) suggests that yield strength (ksi) for A36 grade steel is normally distributed with mean = 43 and standard deviation = 4.5.(a) What is the probability that yield strength is greater than 58?
(b) What yield strength value separates the strongest 75% from the others?
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…
A recent poll found that
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N
Event
Sample p
95% CI for p
1026
664
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0.676413)
Question content area bottom
b. Suppose a sports blogger wrote an article claiming that a majority of adults from this country believe that colleges and universities with big sports programs place too much emphasis on athletics over academics. Does this confidence interval support the blogger's claim? Explain your reasoning.
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B.
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C.
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Chapter 11 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 11.1 - An experiment was carried out to investigate the...Ch. 11.1 - Four different coatings are being considered for...Ch. 11.1 - Prob. 3ECh. 11.1 - In an experiment to see whether the amount of...Ch. 11.1 - In an experiment to assess the effect of the angle...Ch. 11.1 - A particular county employs three assessors who...Ch. 11.1 - Prob. 7ECh. 11.1 - The paper Exercise Thermoregulation and...Ch. 11.1 - The article The Effects of a Pneumatic Stool and a...Ch. 11.1 - Prob. 10E
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 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 - Prob. 17ECh. 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 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.3 - The output of a continuous extruding machine that...Ch. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Nickel titanium (NiTi) shape memory alloy (SMA)...Ch. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - The article The Responsiveness of Food Sales to...Ch. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 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 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 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 - Prob. 46ECh. 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 - Prob. 51SECh. 11 - Prob. 52SECh. 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 - Prob. 57SECh. 11 - Prob. 58SECh. 11 - The bond strength when mounting an integrated...Ch. 11 - Prob. 60SECh. 11 - Prob. 61SE
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A manufacturer of flashlight batteries claims that the average life of her batteries is larger than 400 hours. Peter, as a quality assurance officer in the manufacturing company, took a random sample of 13 batteries from a day’s production and used them continuously until they failed to work. The lifetime (hours) until failure was:342 426 317 545 264 451 1049 631 512 266 492 562 298
(a) At the 0.05 level of significance, is there evidence that the manufacturer’s claim is correct?
(b) What is the p-value?
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A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is
1.34.
A dietician is asked to test this claim and finds that a random sample of
16
servings has a variance of
1.22.
At
α=0.05,
is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below.
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The article “Monte Carlo Simulation—Tool for Better Understanding of LRFD” (J. of Structural Engr., 1993: 1586–1599) suggests that yield strength (ksi) for A36 grade steel is normally distributed with ? = 43 and ? = 4.5.
a. What is the probability that yield strength is greater than 58?
b. What yield strength value separates the strongest 75% from the others?
c. what is the probability that the thread length of a randomly selected bolt is Within 1.5 SDs of its mean value?
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A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is
1.141.14.
A dietician is asked to test this claim and finds that a random sample of
2424
servings has a variance of
0.950.95.
At
alpha equals 0.10α=0.10,
is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed.
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An article in Technometrics (1999, Vol. 41, pp. 202–211) studied the capability of a gauge by measuring the weights of two sheets of paper. The data follow.
Test the hypothesis that the mean weight of the two sheets is equal (μ1−μ2μ1−μ2)against the alternative that it is not (and assume equal variances). Find the t-stat to 3 decimal places.
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A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.25. A dietician is asked to test this claim and finds that a random sample of 22 servings has a variance of 1.35. At ⍶ = 0.05 is there enough evidence to reject the manufacturer’s claim?
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An electrical engineer wishes to determine if, among two specific municipal buildings in town, Building “North” and Building “South”, whether the tensile strength of pipes (in psi) is not the same in each of these two buildings. A sample of pipes was chosen at random from both Building “North” and Building “South”, respectively.
Using α = 0.05, which of the following statistical test, or parameter, would be best for determining whether tensile strength of pipes (in psi) is not the same in each of these two buildings? (Assume all statistical assumptions met.)
a) Binomial Distribution
b) Population Difference in Means (i.e., Unpaired Data)
c) The Chi-Squared Test of Independence
d) Population Mean Difference (i.e., Paired Data)
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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 proportion of voters favoring a VAT Degrees difference between high and low income voters. (Where P1 is the proportion of all high income voters who is 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
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A researcher conducts an independent- measures research study and obtains t = 2.070 with df = 28.
How many individuals participated in the entire research study?
Using a two- tailed test with α = .05, is there a significant difference between the two treatment conditions?
Compute r2 to measure the percentage of variance accounted for by the treatment effect.
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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.
Leavers
Stayers
1 = 3.09
2 = 2.92
σ1 = 0.78
σ2 = 0.78
n1 = 107
n2 = 222
At α = 0.01, can it be concluded that there is a difference in the self-esteem scores of the two groups? Use the P-value method.
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The following table shows the results of a two-factor analysis of variance with 2 levels of factor A, 3 levels of factor B, and a separate sample of n = 5 participants in each of the treatment conditions. Note that several values are missing in the table. What is the missing value for the F-ratio for the AxB interaction?
Source SS df MS
Between 80 xx
A 8 xx xx F = xx
B xx xx 20 F = xx
AxB xx xx xx F = xx
Within xx xx xx
Total 176 xx
Question options:
a.
4
b.
2
c.
16
d.
8
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The following table shows the results of a screening test hypothesized to detect persons at risk for side effects of a new cosmetic surgery. Compute the specificity of the test.
Side effects present
Side effects absent
Screen positive
12
6
Screen negative
85
204
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