Fasteners used in aircraft manufacturing are slightly crimped so that they lock enough to avoid loosening during vibration. Suppose that 55% of all fasteners pass an initial inspection. Of the 45% that fail, 10% are so seriously defective that they must be scrapped. The remaining fasteners are sent to a recrimping operation, where 40% cannot be salvaged and are discarded. The other 60% of these fasteners are corrected by the recrimping process and subsequently pass inspection. (a) What is the probability that a randomly selected incoming fastener will pass inspection either initially or after recrimping? (b) Given that a fastener passed inspection, what is the probability that it passed the initial inspection and did not need recrimping? (Round your answer to four decimal places.)
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.In North America, between 100 million and 1 billion birds die each year by crashing into windows on buildings, more than any other human-related cause. This figure represents up to 5% of all birds in the area. One possible solution is to construct windows angled downward slightly, so that they reflect the ground rather than an image of the sky to a flying bird. An experiment by Klem et al. (2004) compared the number of birds that died as a result of vertical windows, windows angled 20 degrees off vertical, and windows angled 40 degrees off vertical. The angles were randomly assigned with equal probability to six windows and changed daily; assume for this exercise that windows and window locations were identical in every respect except angle. Over the course of the experiment, 30 birds were killed by windows in the vertical orientation, 15 were killed by windows set at 20 degrees off vertical, and 8 were killed by windows set at 40 degrees off vertical. . Clearly state an appropriate…In North America, between 100 million and 1 billion birds die each year by crashing into windows on buildings, more than any other human-related cause. This figure represents up to 5% of all birds in the area. One possible solution is to construct windows angled downward slightly so that they reflect the ground rather than an image of the sky to a flying bird. An experiment by Klem et al. (2004) compared the number of birds that died as a result of vertical windows, windows angled 20 degrees off vertical, and windows angled 40 degrees off vertical. The angles were randomly assigned with equal probability to six windows and changed daily; assume for this exercise that windows and window locations were identical in every respect except angle. Over the course of the experiment, 30 birds were killed by windows in the vertical orientation, 15 were killed by windows set at 20 degrees off vertical, and 8 were killed by windows set at 40 degrees off vertical. a. Clearly state an appropriate…
- We're interested in whether warm milk helps people go to sleep faster. We have a lab with EEG monitors that will provide us with data as to how many minutes elapse before someone falls asleep. (People spend the night in the lab.) In the first experimental condition, participants fall asleep as they usually do, without warm milk. In the second condition, participants drink 6 oz. of warm milk before going to sleep. Data for 5 participants is shown in the table below. Choose the appropriate type of t- test (independent samples or paired samples) and conduct the t-test and hypothesis test. Be sure to show all of your calculations either on your scratch work or in this text box. DO: Include the t-test value and your hypothesis test conclusion in this test box, not just in your scratch work. Minutes to Minutes to NO MILK sleep MILK sleep Participant 1 10 Participant 1 11 Participant 2 10 Participant 2 12 Participant 3 8. Participant 3 8 Participant 4 17 Participant 4 13 Participant 5 13…We’re interested in whether warm milk helps people go to sleep faster. We have a lab with EEG monitors that will provide us with data as to how many minutes elapse before someone falls asleep. (People spend the night in the lab.) In the first experimental condition, participants fall asleep as they usually do, without warm milk. In the second condition, participants drink 6 oz. of warm milk before going to sleep. Data for 5 participants is shown in the table below. Choose the appropriate type of t-test (independent samples or paired samples) and conduct the t-test and hypothesis test. Be sure to show all of your calculations either on your scratch work or in this text box. DO: Include the t-test value and your hypothesis test conclusion in this text box, not just in your scratch work.An analysis of first-year students at a college revealed that 1/5 of the first-year women were from homes where both parents were professionals. Of these, 3/4 were interested in the same profession as one or both of their parents. If this latter group is made up of 15 students, how many first-year women are there?
- Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 17 specimens of a particular species, 6 resprouted after fire. Estimate with 95% confidence the proportion of all shrubs of this species that will resprout after fire.Interval:The specification for the pull strength of a wire that connects an integrated circuit to its frame is 10 g or more. Units made with aluminum wire have a defect rate of 10%. A redesigned manufacturing process, involving the use of gold wire, is being investigated. The goal is to reduce the rate of defects to 5% or less. Out of the first 100 units manufactured with gold wire, only 4 are defective. True or false: a) Since only 4% of the 100 units were defective, we can conclude that the goal has been reached. b) Although the sample percentage is under 5%, this may represent sampling variation, so the goal may not yet be reached. c) There is no use in testing the new process, because no matter what the result is, it could just be due to sampling variation. d) If we sample a large enough number of units, and if the percentage of defective units is far enough below 5%, then it is reasonable to conclude that the goal has been reached.In an effort to link cold environments with hypertension in humans, a preliminary experiment was conducted to investigate the effect of cold on hypertension in rats. Two random samples of 6 rats each were exposed to different environments. One sample of rats was held in a normal environment at 26°C. The other sample was held in a cold 5°C environment. Blood pressures and heart rates were measured for rats for both groups. The blood pressures for the 12 rats are shown in the table below. a. Provide a 95% confidence interval on the difference in the two population meansb. Do the data provide sufficient evidence that rats exposed to a 5°C environment have a higher mean blood pressure than rats exposed to a 26°C environment? Use α = 0.05
- The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because plants use CO2 to fuel photosynthesis, more CO, may cause trees and other plants to grow faster. An elaborate apparatus allows researchers to pipe extra CO, to a 30-meter circle of forest. They selected two nearby circles in each of three parts of a pine forest and randomly chose one of each pair to receive extra CO,. The response variable is the mean increase in base area for 30 to 40 trees in a circle during a growing season. We measure this in percent increase per year. Here are one year's data. Control plot - Control Treated plot 10.547 Pair Treated 9.732 0.815 7.273 9.244 1.971 5.762 8.675 2.913 (a) State the null and alternative hypotheses. (Where u is the mean difference, treated minus control.) Но: и На: и Explain clearly why the investigators used a one-sided alternative. The researchers have no preconceived idea what extra CO, will do to the growth rate.…Three different corrosion-resistant coatings are being considered for use on iron pipes. Ten pieces of pipe are marked off in six equal segments. For each pipe, two segments received coating A, two received coating B, and the remaining two received coating C. The pipes were placed in a corrosive environment for a period of time; then the depth of the deepest pit (in mm) caused by corrosion was measured for each segment on each pipe. The effect of interest is the coating; the pipe is a blocking factor, and there were two replications on each pipe. The following sums of squares were calculated: sum of squares for blocks = 11.2, sum of squares for treatments = 4.8, sum of squares for interactions = 18.4, total sum of squares = 44.7. a) Construct an ANOVA table. You may give ranges for the P-values. b) Are the assumptions for a randomized complete block design satisfied? Explain. c) Does the ANOVA table provide evidence that mean pit depth differs among coatings? Explain.Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?