Concept explainers
A regular type of laminate is currently being used by a manufacturer of circuit boards. A special laminate has been developed to reduce warpage. The regular laminate will be used on one sample of specimens and the special laminate on another sample, and the amount of warpage will then be determined for each specimen. The manufacturer will then switch to the special laminate only if it can be demonstrated that the true average amount of warpage for that laminate is less than for the regular laminate. State the relevant hypotheses, and describe the type I and type II errors in the context of this situation.
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Chapter 8 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- ABC Cookie Company takes samples of finished boxes of cookies weighing them to make sure the weight filled stays within the targeted amount. Some variation of course, is to be expected. But too much presents a production issue. Your job is to find out if this process is stable enough to continue. Samples are taken for 20 days. The number of boxes checked each day is 100. The 20 samples measured reveal the following proportions found to have defective weights: Sample Number Of Defectives Proportion Defective 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 6 0.06 0 0.00 4 0.04 10 0.10 6 0.06 4 0.04 12 0.12 10 0.10 8 0.08 10 0.10 12 0.12 10 0.10 14 0.14 8 0.08 6 0.06 16 0.16 12 0.12 14 0.14 20 0.20 18 0.18 Complete the following: Calculate the centerline (CL), upper control limit (UCL), and the lower control limit (LCL) for a P- Chart. You can use the Excel template to work through this problem. Create a control chart, showing the CL, LCL, and…arrow_forwardPlease show me your solutions and interpretations. Show the completehypothesis-testing procedure.A manufacturing company produces bearings. One line of bearings is specified to be 1.64 centimeters (cm) in diameter. A major customer requires that the variance of the bearings be no more than 0.001 cm2. The producer is required to test the bearings before they are shipped, and so the diameters of 16 bearings are measured with a precise instrument, resulting in the following values:1.69 1.62 1.63 1.70 1.66 1.63 1.65 1.71 1.64 1.69 1.57 1.64 1.59 1.66 1.63 1.65Assume bearing diameters are normally distributed. Use the data and α = 0.025 to test the data to determine whether the population of these bearings is to be rejected because of too high variance.arrow_forwardA manufacturing company would like to investigate the effect of a new supplier of raw material to their product. The company makes 4,000 of these items each day and the new supplier is much less expensive than their current supplier. If the rate of defects remains unchanged with the new material, they will use the new material. For their analysis, they take a cluster sample of 500 items made from the new supplier's material. The company knows their supplied product has a defect rate of 6.5%. Regardless of whether the conditions are met: What is the standard deviation of the sampling distribution? Report 4 decimals. Do not use % (ex. good answer is .0234)arrow_forward
- The Us food and Drug administration has a limit for mercury content in fish of 1.0ppm (parts per million) while in Canada the limit is 0.5 ppm. Using the variable average mercury in the Florida lakes dataset to test whether there is evidence that average mercury level of fish ( large mouth Bass) in Florida lakes is less than 1.0ppm and whether there is evidence that average mercury level of fish in Florida lakes is less than 0.5ppm. STATE THE NULL AND ALTERNATIVE HYPOTHESES? GIVE THE TEST STATISTICS AND P-VALUE? round the test statistic to two decimal places and the p-value to three decimal places. DOES THIS SAMPLE PROVIDE EVIDENCE THAT THE AVERAGE MERCURY LEVEL OF FISH (LARGE MOUTH BASS) IN FLORIDA LAKES IS LESS THAN 1.0PPM? LESS THAN 0.5 PPM : STATE THE NULL AND ALTERNATIVE HYPOTHESES. GIVE THE TEST STATISTICS AND P-VALUE ? round the test statistic to two decimal places and the p-value to three decimal places. DOES THIS SAMPLE PROVIDE EVIDENCE THAT THE AVERAGE MERCURY…arrow_forwardA study published by Babcock and Marks (2010) showed that the average full-time U.S. college student studied for μ = 14 hours per week (SD = 4.8 hours per week) in 2005. We want to know if this average has changed in the past 15 years. In other words, we are going to do a study in which we try to determine whether there has been an impact of the passage of time on the amount of time college students spend studying. We selected a sample of n = 64 of today’s college students and find that they spent an average of M = 12.5 hours per week studying. Does this sample indicate a significant change in the number of hours spent studying? Use a two-tailed test (this means non-directional hypothesis) with α = .05.arrow_forwardWorkers in the office like to drink coffee during work. A doctor is concerned about this situation since the too much coffee consumption may result to long-term health problems. However, studies suggests that there is no risk in drinking three cups of coffee per day, which is about 250 mg of caffeine. The doctor wants to know if the amount of caffeine consumed by the workers is within tolerable limits. He randomly selected 20 students and found that they consume an average of 270 mg of caffeine each day with a standard deviation of 48 mg. Assume that the daily amount of caffeine consumed by students follow the normal distribution.1. Which of the following sets of hypotheses should be used in this study? A. Ho: μ = 250 vs. Ha: μ > 250 B. Ho: μ ≤ 250 vs. Ha: μ > 250 C. Ho: μ = 270 vs. Ha: μ > 270 D. Ho: μ = 270 vs. Ha: μ ≠ 270 2. Which of the following is(are) TRUE? I. The appropriate test procedure to answer the objective of the study is a…arrow_forward
- 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…arrow_forwardCadmium,aheavymetal,istoxictoanimals. Mushrooms,however,areabletoabsorband accumulate cadmium at high concentrations. The Czech and Slovak governments have set a safety limit for cadmium in dry vegetables at 0.5 parts per million (ppm). M. Melgar et al. measured the cadmium levels in a random sample of the edible mushroom Boletus pinicola and published the results in a paper. Here are the data: 0.24 0.59 0.62 0.16 0.77 1.33 0.92 0.19 0.33 0.25 0.59 0.32 At the 5% significance level, do the data provide sufficient evidence to conclude that the mean cadmium level in Boletus pinicola mushrooms is greater than the government’s recommended level of 0.5 ppm? Assume that the population standard deviation of cadmium levels in Boletus pinicola mushrooms is 0.37 ppm (Note: The sum of the data is 6.31 ppm.)arrow_forwardAn army depot that overhauls ground mobile radar systems is interested in improving its processes. One problem involves troubleshooting a particular component that has a high failure rate after it has been repaired and reinstalled in the system. The shop floor supervisor believes that having standard work procedures in place will reduce the time required for troubleshooting this component. Time (in minutes) required troubleshooting this component without and with the standard work procedure is recorded for a sample of 19 employees. Assuming that we define our differences as Time without standard work procedure - Time with standard work procedure, and the p-value associated with the test statistic is less than 0.0001. At alpha = 0.05, I. we reject the null hypothesis II. we fail to reject the null hypothesis III. we can conclude that having standard work procedures in place reduces troubleshooting time for this component I only II only III only…arrow_forward
- To illustrate the effects of driving under the influence (DUI) of alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine teenagers, the time (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded. Complete parts (a) and (b). Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Click the icon to view the data table. (a) Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the experiment? A. This is a good idea in designing the experiment because it controls for any "learning" that may occur in using the simulator. B. This is a good idea in designing the experiment because…arrow_forwardTo illustrate the effects of driving under the influence (DUI) of alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine teenagers, the time (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded. Complete parts (a) and (b). Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Click the icon to view the data table. (a) Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the experiment? O A. This is a good idea in designing the experiment because the sample size is not large enough. B. This is a good idea in designing the experiment because it controls for any "learning"…arrow_forwardTo illustrate the effects of driving under the influence (DUI) of alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine teenagers, the time (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded. Complete parts (a) and (b). Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. (a) Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the experiment? A.This is a good idea in designing the experiment because the sample size is not large enough. B. This is a good idea in designing the experiment because it controls for any "learning" that may occur in…arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill