Three engineers are independently estimating the spring constant of a spring, using the linear model specified by Hooke’s law. Engineer A measures the length of the spring under loads of 0, 1, 3, 4, and 6 lb, for a total of five measurements. Engineer B uses the same loads, but repeats the experiment twice, for a total of 10 independent measurements. Engineer C uses loads of 0, 2, 6, 8, and 12 lb, measuring once for each load. The engineers all use the same measurement apparatus and procedure. Each engineer computes a 95% confidence interval for the spring constant.
- a. If the width of the interval of engineer A is divided by the width of the interval of engineer B, the quotient will be approximately______.
- b. If the width of the interval of engineer A is divided by the width of the interval of engineer C, the quotient will be approximately________.
- c. Each engineer computes a 95% confidence interval for the length of the spring under a load of 2.5 lb. Which interval is most likely to be the shortest? Which interval is most likely to be the longest?
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Statistics for Engineers and Scientists
Additional Math Textbook Solutions
Statistics for Psychology
STATISTICS F/BUSINESS+ECONOMICS-TEXT
Elementary Statistics: Picturing the World (7th Edition)
Statistical Techniques in Business and Economics
Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
Elementary Statistics Using The Ti-83/84 Plus Calculator, Books A La Carte Edition (5th Edition)
- A manufacturer of cases for sound equipment requires drilling holes for metal screws. The drill bits wear out and must be replaced; there is expense not only in the cost of the bits but also for lost production. Engineers varied the rotation speed of the drill and measured the life- time y of four bits at each of five speeds. Speed Lifetime 60 4.6 60 3.8 60 4.9 60 4.5 80 4.7 80 5.8 80 5.5 80 5.4 100 5 100 4.5 100 3.2 100 4.8 120 4.1 120 4.5 120 4 120 3.8 140 3.6 140 3 140 3.5 140 3.4 Create a scatterplot of the data. Does there appear to be a relation? Does it appear to be linear? Regardless fit a simple linear regression model to the data. What can you say about the fit of the model to the data? Is there any evident outlier . Remove this observation and fit the regression model again. Is it improving the model farrow_forwardWhich of the following difperen tial equations are s eperable. Select all that apply A. =-3y B. dy tyry C. dy = D. dy dt %1 E. None of the a bovearrow_forwardHooke's Law states that the length a spring stretches is directly proportional to the weight on the spring. If a weight of 5 kg stretches a spring 12 cm, determine the weight that would stretch the spring 27 cm. O 2.22 kg O 64.8 kg O 11.25 kg O cannot be determined with the information givenarrow_forward
- Answer using newton Raphson method by step...arrow_forward#15. Calculate the ideal body weight in pounds and kilograms for an 87-year-old female patient who is 5 feet 1 inch tall and weighs 111 lb.arrow_forwardA manufacturer of cases for sound equipment requires that holes be drilled for metal 11.9 screws. The drill bits wear out and must be replaced; there is expense not only in the cost of the bits but also in the cost of lost production. Engineers varied the rotation speed of the drill and measured the lifetime y (thousands of holes drilled) of four bits at each of five speeds x. The data were: 60 60 60 60 80 80 80 80 100 100 y 4.6 3.8 4.9 4.5 4.7 5.8 5.5 5.4 5.0 4.5 100 100 120 120 120 120 140 140 140 140 y 3.2 4.8 4.1 4.5 4.0 3.8 3.6 3.0 3.5 3.4 a. Create a scatterplot of the data. Does there appear to be a relation? Does it appear to be linear? b. Is there any evident outlier? If so, does it have high influence? ? IIarrow_forward
- A cable 200 ft long and weighing 4 Ib/ft is hanging vertically down a well. If a weight Of 100 lbs is suspended from the lower end of the cable, find the work done in pulling the cable and weight to the top of the well. a. 120000 ft-lb O b. 80000 ft-lb O c. 100000 ft-lb O d. 90000 ft-lb e. None of the choices.arrow_forwardAn unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that expresses mass as a function of the volume. grams Volume in ml 15 289.8 17.5 331.3 nces 20 386.4 22.5 426 ations 487.8 25 27.5 520.7 Drive 30 591.2 365 A) Write the linear regression equation for the data in the chart. t Course tions Volume = where x is the grams of the unknown metal. Round your answers to 3 decimal places B) If the mass of an unknown metal is 13, using your un-rounded regression equation find its predicted volume. Round your answer to 1 decimal place. Question Help: O Message instructor Submit Question Type here to search B Narrow_forwardAn engineer was interested in the effect of two factors on strength of sheet castings of a polymer. One factor was time in a polymerization bath with 1% catalyst. The other factor was the temperature of the polymerization bath. The engineer tried two times (20 minutes and 60 minutes) and two temperatures (100 and 120 degrees F). He treated samples of polymer under each of the four sets of conditions. Then he measured flexural strength (in pounds per square inch, or psi) on samples of sheet castings of the polymer. The results are shown in the table below: 100 degrees 20 minutes 9500 10650 9700 9950 10100 60 minutes 11500 11650 11250 11250 11900 120 degrees 11300 11750 11600 11650 11700 10900 11500 11850 11700 11650 Test for main factor effects or factor interactions, at the 5% significance level.arrow_forward
- A tank full of water. Find the work required to pump the water out of the spout.arrow_forward31. Let arc TF = 14", arc FH = 27', arc HN = 114°, and arc NO = 65°, in O J. J T L N Farrow_forwardA math professor selects 8 students at random from her calculus class and asks them to record their study times. After two weeks, she gives an exam. the number of hours, x, of study time and the test score, y, yield the following sample data summary: Ex = 117 Ey = 660 8 %3| n 3= Ea2 = 1869 54638 9519 The professor is a bit surprised. a) Find the equation of the regression line. b) Use the regression line to predict the score of a student who studies for 20 hours over the two weeks.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage