Six different machines are being considered for use inmanufacturing rubber seals. The machines are being comparedwith respect to tensile strength of the product. A random sampleof four seals from each machine is used to determine whether themean tensile strength varies from machine to machine. Thefollowing are the tensile-strength measurements in kilograms persquare centimeter x 10-1:Machine3420.314.615.716.717.820.818.618.918.920.5 20.1Perform the analysis of variance at the 0.05 level of significanceand indicate whether the mean tensile strengths differ significantlyfor the six machines.117.516.915.8216.419.217.715.4517.519.216.5618.316.217.5

Given data: 1 2 3 4 5 6 17.5 16.4 20.3 14.6 17.5 18.3 16.9 19.2 15.7 16.7 19.2 16.2 15.8…

Answered: Six different machines are being…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The quality control engineer at Palmer Industries is interested in estimating the tensile strength of steel wire based on its outside diameter and the amount of molybdenum in the steel. As an experiment, she selected 25 pieces of wire, measured the outside diameters, and determined the molybdenum content. Then she measured the tensile strength of each piece. The results of the first four are recorded in the table. Tensile Strength Outside Diameter Amount of Molybdenum Place (PSI ) Y (mm) X1 (Units) X2 A 11 0.3 6 B 9 0.2 5 C 16 0.4 8 D 12 0.3 7 Using a statistical software package, the QC engineer determined the multiple regression equation to be Y’=-0.5+20X1+1X2. a) Based on the equation, what is the estimated tensile strength of a steel wire having an outside diameter of .35 mm and 6.4 units of molybdenum? b) Interpret the value of b1 in the equation.
How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Students doing a laboratory exercise sample 20 pieces of wood and find an average load capacity of 30,841 pounds. We are willing to regard the wood pieces prepared for the lab session as an SRS of all similar pieces of Douglas fir. Engineers also commonly assume the characteristics of materials vary normally. Suppose that the strength of pieces of wood like these follow a normal distribution with a population standard deviation of 3,000 pounds (As you can see all three necessary assumptions are met). a. Assuming that all evergreen wood has a known "load" capacity average of 30,000 pounds. Make a two-sided hypothesis (null and alternative statement) about Douglas Fir "load" capacity compared to the overall average. b. Apply the formula for finding our test statistic (show your work or describe the process) Specifically, use the formula for the z-statistic (pasted below and on…
Tennis elbow is thought to be aggravated by the impact experienced when hitting the ball. The article Forces on the Hand in the Tennis One-Handed Backhand reported the force (Newtons) on the hand just after impact on a one-handed backhand drive for six advanced players and for eight intermediate players. Type Of player Size Mean SD Advanced 8 45.3 12.1 Intermediate 10 22.4 10.2 1) Calculate a 95% CI for the difference of true average for advanced players (µ1) and the true average for intermediate players (µ2). 2) Does your interval provide good evidence for concluding that the two µs are different? 3) Would you have reached the same conclusion by calculating a CI for µ2 − µ1 (i.e., by reversing the 1 and 2 labels on the two types of players)? Explain
2. Three tensile tests were carried out on an aluminum bar. In each test, the strain was measured at the same values of stress. The results were Stress (MPa) 34.5 69.0 103.5 138.0 Strain (Test 1) 0.46 0.95 1.48 1.93 Strain (Test 2) 0.34 1.02 1.51 2.09 Strain (Test 3) 0.73 1.10 1.62 2.12 Where the units of strain are mm/m. Use linear regression to estimate the modulus of elasticity of the bar (modulus of elasticity = stress/strain). %3D
Glaucoma is a leading cause of blindness in the United States, N. Ehlers measured the difference in corneal thickness (in microns) between the two eyes of eight patients. Each patient had one eye that had glaucoma and one eye that was normal. The difference was measured as the corneal thickness of normal eye – corneal thickness of eye with Glaucoma. Corneal thickness is important because it can mask an accurate reading of eye pressure. Use ? = .05. Q) If a participant has the same corneal thickness in their normal eye as the eye with Glaucoma, what would be the value for difference: measured as the corneal thickness of normal eye – corneal thickness of eye with Glaucoma.
To assess the strength of the recycled concrete aggregated products, the measurements of the resiliency modulus (MPa) were collected on 20 selected specimens. Identify the unit, population of units, variable of interest, statistical population, and sample.
Glaucoma is a leading cause of blindness in the United States, N. Ehlers measured the difference in corneal thickness (in microns) between the two eyes of eight patients. Each patient had one eye that had glaucoma and one eye that was normal. The difference was measured as the corneal thickness of normal eye – corneal thickness of eye with Glaucoma. Corneal thickness is important because it can mask an accurate reading of eye pressure. Use ? = .05. Hypothesis: H0: μd=0Ha: μd≠0 Using output Test statistics : t=0.134P value=0.897 Degrees of freedom (df): df=7 Level of significance: α=0.05 Decision: P value > 0.05 thus we fails to reject null hypothesis. Question a)Write a report summarizing your findings. When writing the report consider that medical staff estimate that a difference of 4.5 microns or more could impact on their ability to interpret eye pressure correctly. b) Define for the hypothesis stated in part b) what a type 1 error and type 2 error would mean. Is it possible…
Glaucoma is a leading cause of blindness in the United States, N. Ehlers measured the difference in corneal thickness (in microns) between the two eyes of eight patients. Each patient had one eye that had glaucoma and one eye that was normal. The difference was measured as the corneal thickness of normal eye – corneal thickness of eye with Glaucoma. Corneal thickness is important because it can mask an accurate reading of eye pressure. Use ? = .05 H0: μd=0 H1: μd≠0 T statistic: t = 1.053, P value = 0.327 Degrees of Freedom n-1 = 8-1= 7 critical value 2.3646 If t is less than 2.3646, or greater than 2.3646, reject the null hypothesis Level of significance: α=0.05 question: what a type 1 error and type 2 error would mean. Is it possible that we could have committed a type 2 error in conducting the test
Glaucoma is a leading cause of blindness in the United States, N. Ehlers measured the difference in corneal thickness (in microns) between the two eyes of eight patients. Each patient had one eye that had glaucoma and one eye that was normal. The difference was measured as the corneal thickness of normal eye – corneal thickness of eye with Glaucoma. Corneal thickness is important because it can mask an accurate reading of eye pressure. Use ? = .05. If a participant has the same corneal thickness in their normal eye as the eye with Glaucoma, what would be the value for difference: measured as the corneal thickness of normal eye – corneal thickness of eye with Glaucoma.
Glaucoma is a leading cause of blindness in the United States, N. Ehlers measured the difference in corneal thickness (in microns) between the two eyes of eight patients. Each patient had one eye that had glaucoma and one eye that was normal. The difference was measured as the corneal thickness of normal eye – corneal thickness of eye with Glaucoma. Corneal thickness is important because it can mask an accurate reading of eye pressure. Use ? = .05. Q)Conduct a hypothesis test to determine if there is sufficient evidence to conclude that corneal thickness is different in normal eyes compared to eyes with glaucoma? Write up your results using the 8 steps.
A water hose manufacturer has developed a light-weight hose for home owners. Besides being constructed of a lightweight material. one of the characteristics of the hose is that it shrinks when it is not in use. When in use, the length of hose extends to its advertised length of 50 feet. Twenty hoses are tested to see if the hoses extend to the length of 50 feet. The sample mean of the length of the hoses is 49 1/2 feet with a s of 15 inches. Test the hypothesis at alpha = .01 that the hoses are not equal to 50 feet.
The "spring-like effect" in a golf club could be determined by measuring the coefficient of restitution (the ratio of the outbound velocity to the inbound velocity of a golf ball fired at the clubhead). Twelve randomly selected drivers produced by two clubmakers are tested and the coefficient of restitution measured. The data follow: Club 1: 0.8406, 0.8104, 0.8234, 0.8198, 0.8235, 0.8562, 0.8123, 0.7976, 0.8184, 0.8265, 0.7773, 0.7871 Club 2: 0.8305, 0.7905, 0.8352, 0.8380, 0.8145, 0.8465, 0.8244, 0.8014, 0.8309, 0.8405, 0.8256, 0.8476 Test the hypothesis that both brands of ball have equal mean overall distance. Use α = 0.05 and assume equal variances. Question: Reject H0 if t0 < ___ or if t0 > ___.

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