A mechanical engineer wishes to compare strength properties of steel beams with similar beams made with a particular alloy. The same number of beams, n, of each type will be tested. Each beam will be set in a horizontal position with a support on each end, a force of 2500 lb will be applied at the center, and the deflection will be measured. From past experience with such beams, the engineer is willing to assume that the true standard deviation of deflection for both types of beam is .05 in. Because the alloy is more expensive, the engineer wishes to test at level .01 whether it has smaller average deflection than the steel beam. What value of n is appropriate if the desired type II error probability is .05 when the difference in true average deflection favors the alloy by .04 in.?
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Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
- The data sheet labeled rebound comes from a company which supplies a major automobile manufacturer with shock absorbers. A major quality characteristic of interest is the “force transferred through the shock absorber when the shank is forced out of the cylinder”. The exact technical definition of this test is not important for us. What we do need to understand is that the manufacturer only considers the shock to be an acceptable part if the force measurement is between 485 and 585.The shock manufacturer and the auto manufacturer are arguing over the following issue. Before the shock is finally shipped, it is filled with gas. After it is filled with gas it becomes very difficult to measure the force quantity we are interested in. The shock makers would like to make themeasurement before the shock is filled with gas. The auto maker is concerned that there may be a difference in the force before and after the shock is filled with gas and so would like to make the measurement after it is…arrow_forwardA consumer agency is investigating the blowout pressures of Soap Stone tires. A Soap Stone tire is said to blow out when it separates from the wheel rim due to impact forces usually caused by hitting a rock or a pothole in the road. A random sample of 28 Soap Stone tires were inflated to the recommended pressure, and then forces measured in foot-pounds were applied to each tire (1 foot-pound is the force of 1 pound dropped from a height of 1 foot). The customer complaint is that some Soap Stone tires blow out under small-impact forces, while other tires seem to be well made and don't have this fault. For the 28 test tires, the sample standard deviation of blowout forces was 1358 foot-pounds. Soap Stone claims its tires will blow out at an average pressure of 24,000 foot-pounds, with a standard deviation of 1020 foot-pounds. The average blowout force is not in question, but the variability of blowout forces is in question. Using a 0.01 level of significance, test the claim that the…arrow_forwardNeed help on part D! How does lateral acceleration—side forces experienced in turns that are largely under driver control—affect nausea as perceived by bus passengers? An article reported data on x = motion sickness dose (calculated in accordance with a British standard for evaluating similar motion at sea) and y = reported nausea (%). Relevant summary quantities are n = 17, xi = 223.9 , yi = 196 , xi2 = 3056.65 , xiyi = 2759.6 , yi2 = 2976 . Values of dose in the sample ranged from 6.0 to 17.6. (a) Assuming that the simple linear regression model is valid for relating these two variables (this is supported by the raw data), calculate and interpret an estimate of the slope parameter that conveys information about the precision and reliability of estimation. (Calculate a 95% CI. Round your answers to three decimal places.) , (b) Does it appear that there is a…arrow_forward
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- What parameter is being tested?arrow_forwardThe "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 > ___.arrow_forwardThe authors of a paper compared two different instruments for measuring a person's capacity for breathing out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter. The Wright meter is thought to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. Use of the mini-Wright meter could be recommended as long as there is not convincing evidence that the mean reading for the mini-Wright meter is different from the mean reading for Wright meter. For purposes of this exercise, you can assume that it is reasonable to consider the 17 people who participated in this study as representative of the population of interest. Data values from this paper are given in the accompanying table.…arrow_forward
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