13 20 Selecting the best wafer-slicing machine. Silicon wafer slicing is a critical step in the production of semiconductor devices (e.g.. diodes, solar cells, transistors). Yuanpei (China) University researchers used control charts to aid in selecting the best silicon wafer-slicing machine (Computers & Industrial Engineering, Vol. 52, 2007). Samples of n = 2 wafers were sliced each hour for 67 consecutive hours and bow measurements (a measure of precision) were recorded. The resulting
- a. If the process is in control, what is the probability that a mean bow measurement for a randomly selected hour will fall above the upper control limit?
- b. If the process is in control, what is the probability that 3 of 67 mean bow measurements fall above the upper control limit?
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Statistics for Business and Economics (13th Edition)
- Studies of the size and range of wild animal populations often involve tagging observed individual animals and recording how many times each is caught in a trap (from which it is then released back into the wild). The dataset presented in Table 3 consists of the numbers of times each of n = 334 wood mice were caught in a particular trap (over a two-year time period). The data are also provided in the Minitab file wood-mice.mwx. Table 3 Numbers of trappings of wood mice Times trapped 1 2 Frequency 3 4 5 6 7 8 9 71 59 41 39 20 26 19 12 9 Times trapped 10 11 12 13 14 Frequency 5 15 16 17 18 8 49 2 13 3 3 The geometric distribution with parameter p is a good model for these data. (i) What is the maximum likelihood estimator of p for a geometric model? (ii) What is the maximum likelihood estimate of p for the data in Table 3? You are recommended to use Minitab to help you to answer this part of the question.arrow_forwardBackground: To prevent crashes caused by running red lights, many states are installing cameras at dangerous intersections. These cameras are used to take photographs of the license plates of vehicles that run a red light. The Virginia Department of Transportation (VDOT) obtained data on the number of crashes per year caused by running a red light at 13 intersections in Fairfax County, Virginia. RED LIGHT PHOTO ENFORCED Source: Virginia Transportation Research Council, "Research Report: The Impact of Red Light Cameras (Photo-Red Enforcement) on Crashes in Virginia", June 2007 Directions: Perform an appropriate significance test to determine whether or not the reduction in the number of crashes was statistically significant. 1. Click on the Data button below to display the data. Copy the data into a statistical software package and click the Data button a second time to hide it. Data Before After 3.7 1.26 0.37 0.1 0.39 0 4.55 1.69 2.4 1.94 2.09 3.24 2.5 2.72 0.83 0.24 3.05 1.67 3.21…arrow_forwardProposing a two-factor design. A paint supplier is interested in assessing the hardness of four brands of paint, each with and without an additive that is supposed to add durability. The supplier has a total of 40 panels that can be painted. Hardness will be measured after 180 days of weathering, using an automatic scratch hardness tester. Propose a two-factor design to use for this study, using a two-way table.arrow_forward
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- The authors of a paper compared two different methods for measuring body fat percentage. One method uses ultrasound, and the other method uses X-ray technology. Body fat percentages using each of these methods for 16 athletes (a subset of the data given in a graph that appeared in the paper) are given in the accompanying table. You can assume that the 16 athletes who participated in this study are representative of the population of athletes. Athlete X-ray Ultrasound 1 5.00 4.25 2 15.00 11.75 3 9.25 9.00 4 12.00 11.75 5 17.25 17.00 6 29.50 27.50 7 5.50 6.50 8 6.00 6.75 9 8.00 8.75 10 15.50 16.50 11 9.25 9.50 12 11.00 12.00 13 12.00 12.25 14 14.00 15.50 15 17.00 18.00 16 18.00 18.25 Use these data to estimate the difference in mean body fat percentage measurement for the two methods.arrow_forward6. A major car manufacturer wants to test a new engine to determine whether it meets new air pollution standards. The mean emission, u of all engines of this type must be approximately 20 parts per million of carbon. If it is higher than that, the manufacturer will have to redesign parts of the engine. Ten engines are manufactured for testing purposes, and the emission level of each is determined. Based on data collected over the years from a variety of engines, it seems reasonable to assume that emission levels are roughly Normally distributed with o = 3 parts per 3D3 %3D million of carbon. The data result in an average of 22 parts per million. What is the value of the test statistic?arrow_forwardJoan’s nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost estimating purposes, managers use 2 hours of labor time for the planting of a medium sized tree. Actual times from a sample of 10 plantings during the past month are: 1.9, 1.5, 2.6, 2.2, 2.4, 2.3, 2.6, 3, 1.4, and 2.1. With 5% level of significance, the goal is to test to see whether the mean tree planting time differs from 2 hrs. What is the P-value associated with this test?arrow_forward
- Joan's Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost estimating purposes, managers use two hours of labor time for the planting of a medium-sized tree. Actual times from a sample of 10 plantings during the past month follow (times in hours), 2.7 2.2 2.4 3.3 1.6 1.5 2.4 2.5 1.7 2.8 With a 0.05 level of significance, test to see whether the mean tree-planting time differs from two hours. a. State the null and alternative hypotheses. Ho : 4- Select your answer- V2 H, :- Select your answer - V b. Compute the sample mean. (to 2 decimals) c. Compute the sample standard deviation. (to 4 decimals) d. Find the test statistic and p-value. (Use Table 2 in Appendix B.) (to 3 decimals) p-value -Select your answer e. What is your conclusion? We-Select your answer- Vreject the null hypothesis. There-…arrow_forwardV. SYNTHESIS Direction: Tell whether the given value is a statistic or parameter. 1. NCR has 16 cities. 2. The Philippine Senate is composed of 24 senators. • 3. Based on a sample of 900 elementary students, it was found out that 30% of them could not do long division. 4. Jupiter has 79 moons. 5. The teacher randomly selected 35 employees to participate in the sport festarrow_forwardThe authors of a paper compared two different methods for measuring body fat percentage. One method uses ultrasound, and the other method uses X-ray technology. Body fat percentages using each of these methods for 16 athletes (a subset of the data given in a graph that appeared in the paper) are given in the accompanying table. You can assume that the 16 athletes who participated in this study are representative of the population of athletes. Athlete X-ray Ultrasound 1 5.00 4.50 2 15.00 11.75 3 9.25 9.00 4 12.00 11.75 5 17.25 17.00 6 29.50 27.50 7 5.50 6.50 8 6.00 6.75 9 8.00 8.75 10 16.50 17.50 11 9.25 9.50 12 11.00 12.00 13 12.00 12.25 14 14.00 15.50 15 17.00 18.00 16 18.00 18.25 Use these data to estimate the difference in mean body fat percentage measurement for the two methods. Use a confidence level of 95%. (Use ?d = ?X-ray − ?ultrasound. Round your answers to three decimal places.) , % Interpret the interval in…arrow_forward
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