1 p of 9
Information about SMAM 314-Dr. Gruber's Section Instructor: Dr. M. Gruber office 08-3250 Phone [phone] email [e-mail] Web page http://www.rit.edu/~mjgsma/smam314winter00/hw.html (The web page may also be found by going to my home page and clicking on the link for SMAM 314 Winter 2000-2001.) Textbook: Engineering Statistics The Industrial Experience Ostle Turner Hicks Mc Elrath Calculator: You should have a calculator that will obtain means, standard deviations and fit a linear regression line. The TI 82, 83 and 85 do this. If you do not already have such a calculator the TI 83 is a good choice. I will be using one in class. A less expensive alternative is the Sharp EL506L. Some illustrative examples of how to do basic statistical computations can be found at http://www.rit.edu/~jmwsma/courses/SMAM303/pdfs/el506l.pdf. Software: Extensive use of the software package Minitab will be used. It is available for both Mac and PC in the bookstore for about $100. It may also be used on the VAX(You need an account number.) or it is available on the Macintosh computers in the laboratory on the first floor of the new building. Any version of Minitab will do. Course of Study: An introduction to basic Probability and Statistics for engineering applications. Some use will be made of the statistical software package Minitab. The bulk of Chapters 1-8 will be covered. Homework: Under Assignments there are suggested problems for each section of the text that will be covered in the course. These will not be collected but the problems students have difficulty with and some of the others will be discussed in class. There are ten graded homework assignments. These are to be handed in on the indicated due dates. The best eight grades count 15% of the final grade. Warning: The graded problems do not provide enough practice if you want to do well on the examinations so you must attempt all of the ungraded exercises as well. Homework is the basis for most of the test questions Examinations: There will be six ten minute quizzes and three one-hour examinations. There will be a two-hour final examination when scheduled during final examination week. The day school exam will be held when scheduled during the final exam period from Feb 22-26. Please note: The last examination period is from 4-6 PM on February 26, 2001. Make your travel plans accordingly. There will be no early examinations. The dates for quizzes and examinations are given below.
Quizzes 12/5, 12/12,1/9, 1/16,1/30, 2/6 Exams: 12/19,1/23, 2/13
Grades: Homework counts 15% of the final grade. The best five quiz grades count 15% of the final grade. Each hour exam counts 15%. The final exam counts 25% but may replace any two items that it is better than. The final exam must be taken in order to pass the course. Homework not handed in on time or a missed examination or quiz counts as a zero. I do not expect to give makeup tests. Comment: I am here to help you learn but you will have to meet me halfway. Please plan to attend all classes, attempt all of the assigned homework and more problems from the text if you have time and take all the quizzes and exams. I will usually be available in my office MTR 1-2 or at Math tutoring from 4-6 PM TR and 4-5 MW and will be happy to help you all I can if you try. The Math Department tutoring room is a good place to do your homework and get help if you get stuck. Take advantage of it!
SMAM 314 Suggested problems
Assignments
p 2 of 9
Chapter 2 2.1 p.59 :2.3 2.2 p.58 :2.5 Also make a stem and leaf display using the first two digits as the stem and the last two digits as the leaves. 2.3: p.61 :2.11 a,b 2.4: p.62-63:2.19, 2.22,2.23, 2.24,2.26,2.27,2.31,2.33,2.38,2.41 2.7-2.9: p.67:2.53, 2.55 Chapter 3 3.1: p.97:3.1, 3.3,3.5,3.6,3.9 3.2: p99: 3.11, 3.13 3.3: p.99:3.15,3.16,3.17,3.19,3.21,3.22,2.23,3.24 3.4: p.100: 3.25, 3.29, 3.33,3.35,3.37,,3.39 3.5: p.101: 3.41,3.49, 3.51,3.53 3.6: p.103:3.57, 3.59,3.65 3.71: p.103-104: 3.68,3.69,3.70,3.71,3.72, 3.73,3.75,3.79, 3.84 3.72: p105: 3.85,3.86,3.87,3.90,3.91 3.74: p. 106: 3.92 Chapter 4 4.1-4.2 :p.133 : 4.1, 4.3, 4.5, 4.7, 4.11,4.13, 4.15, 4.17,4.19 4.3: p.136: 4.29,4.31,4.33,4.35, 4.37, 4.41 4.4: p.140: 4.57, 4.59, 4.61 Chapter 5 5.1: p.166: 5.1,5.3, 5.5, 5.7, 5.9, 5.13, 5.15, 5.19 5.1.3 : p.168: 5.29, 5.30,5.33 5.1.4: p.169: 5.35, 5.37 Chapter 6 6.1: p.213: 6.1, 6.2, 6.4,6.15,6.20,6.21 6.2: p.215: 6.24, 6.25, 6.27,6.29,6.30,6.33,6.35,6.38,6.39, 6.41,6.44 6.3: p218: 6.45,6.47,6.49,6.53, 6,57,6.59 6.5: p.221:6.69, 6.71, 6.73, 6.75, 6.77, 6.79 6.6: p.223: 6.81, 6.84,6.87 6.7: p223: 6.88,6.89, 6.93 6.8: p.224:6.95,6.98
p.3 of 9 Chapter 7 7.1: p.275: 7.1, 7.3, 7.5,7.6, 7.7,7.8,7.9,7.11,7.12,7.13, 7.15,7.17,7.19,7.20, 7.21 7.3: p.280: 7.53, 7.55, 7.62 (use Welch formula mentioned in class), 7.67, 7.69,7.71 7.5: p.286: 7.91, 7.97 7.6: p.287: 7.105, 7.107,,7.113, 7.119 Chapter 8: 8.1: p.322:8.5,8.9,8.11 8.4: p.328,8.36,8.378.44,8.45
Graded Homework Homework 1. Due 12/8 1.Do the following problem by hand with your calculator The following data is on oxidation-induction time (min) for various crankcase oils. 87, 103, 130, 160, 180,195, 132, 145, 211, 105, 145, 153, 152, 138,87, 99,93,119,129 A. Make a stem and leaf display with increment 10. B. Make a histogram with intervals 79.5-99.5,99.5-119.5 etc. C. Does the stem and leaf display and the histogram give you similar impressions about the data. Explain. D. Make a five number summary and a boxplot. Determine whether there are any outliers. 2. Use Minitab to do the following problem. The following data on motor octane ratings for various gasoline blends
88.5 87.8 90.3 92.3 91.8 93.7 87.7 89.9 93.4 90.4 91.6 92.7 83.4 88.3 88.5 90.1 90.4 92.2 86.7 87.6 90.1 93.0 91.1 92.2 87.5 84.3 89.2 88.7 92.6 91.2 91.5 86.6 88.3 89.9 89.8 91.0 88.6 100.3 95.6 93.3 88.2 90.8 88.3 98.8 85.3 87.9 88.6 90.9 89.8 89.6 87.4 88.9 90.6 91.1 90.4 89.3 92.2 90.0 90.7 94.7 94.2 89.0 91.2 89.7 91.1 92.7 96.1 89.3 90.3 91.0 93.2 93.3 94.4 91.6 94.2 91 91.8 92.7 90.5
A. Make a stem and leaf display, a five number summary, and a boxplot. Put the data into column 1 of the spreadsheet. Go to session. Use the pull down menu under editor to enable commands. Use the commands stem-and-leaf c1 lvals c1 boxplot c1 You may also use the pull down menus B. Make a histogram. Histogram c1 is the command. C. Use the command describe c1. D. How does the five number summary obtained using the lvals command differ from that obtained using the describe command? E. Describe the shape of the data. Does it appear to be symmetric? Bell shaped? F. Based on the appearance of the boxplot are there any outliers? If so which values
are outliers? p.4 of 9 G. How many data points are within 2 standard deviations of the mean? 3 standard deviations. Are your results within the bounds suggested by Chebychev's rule? 2. Due 12/15 Do this problem with your hand held calculator 1. Wood scientists are interested in replacing solid-wood building material by less expensive products made from wood flakes. They collected the following data to examine the relationship between length in inches and strength in pounds per square inch.
Length 5 6 7 8 9 10 11 12 13 14 Strength 446 371 334 296 249 254 244 246 239 234
A. Make a scatterplot to show how length affects strength. Based on your scatterplot (1) Do the variables appear to be positively or negatively correlated? Explain. (2) Does a straight line model appear to be reasonable? B. Find the regression line. (1) Predict the strength of a piece of wood 8.5 inches long. (2) For each of the values what is the difference between the observed and the predicted values? These numbers are called residuals. (3) What is the correlation coefficient? (4) What percentage of the variation is accounted for by the model? C. Based on your answers to A and B comment on the adequacy of the straight line model. Use Minitab to do this problem. 2. For the data in Problem 2.54 in the Textbook. A. Make a scatterplot. Based on your scatterplot (1) Do the variables appear to be positively or negatively correlated? Explain. (2) Does a straight line model appear to be reasonable? B. Find the regression line. (1) What is the correlation coefficient? (2) What percentage of the variation is accounted for by the model? C. Plot the fitted model and the observed data on the same graph. Comment on the fit. D. Based on your answers to A, B and C comment on the adequacy of the straight line model. Put the data in two columns the x values in C1 and the y values in C2. To plot the graph use the command plot c2*c1 To do the regression regress c2 1 c1 To find the correlation coefficient corr c1 c2 You also may use the pull down menus 3. Due 1/5 1. A company uses three different assembly lines A, B and C to manufacture a particular component. Of those manufactured by line A, 5% need rework to remedy a defect, whereas 8% of B's components need rework and 10% of C's components need rework. Suppose that 50% of the components are produced by line A, 30% are produced by line B and 20% come from line C. There is a defective component. Using Bayes theorem find out which line should be investigated first.
p.5 of 9 2. Consider the system of components in the picture below. Components 1 and 2 are connected in parallel so that subsystem works if either 1 or 2 works. Components 3 and 4 are connected in series. That subsystem works if 3 and 4 work. The components work independently of one another and P(component works) = 0.9. What is the probability that the system works?
4 Due 1/12 1. A family has up to four phone lines, a home use line, a business use line, a teen line and a line for internet access. The probability mass function of the number of phone lines the family has is given by x 0 1 2 3 4 f(x) .01 .60 .25 .10 .04 A. What is the cumulative distribution function of random variable X? B. Find P(1 X 3) C. The basic cost for one phone line is $50 per month, 2 phone lines $80 per month, three lines $100 per month and four lines $110 month. per What is the mean and the standard deviation of the amount of money a randomly selected family pays each month? D. Suppose it costs $100 initially to sign up for the telephone service regardless of how many lines the family chose to have. What is the mean and standard deviation of the cost of the phone line for 12 months. (C = 100 + 12y) where y is the basic cost) 2. The time a vacuum cleaner is used by a family per year in hundreds of hours is a random variable with continuous probability density function 0 < x <1 x f(x) = 2 - x 1< x < 2 A. What is the cumulative distribution function of X? B. What is the probability the vacuum cleaner is used between 80 and 120 hours?
C. What is the mean and the standard deviation of X? 5. Due 1/19
p.6 of 9
1. A lot of 500 items has 50 defectives. A sample of size five is drawn. What is the probability that there are at most two defectives in the sample if A. the sampling is done without replacement? B. the sampling is done with replacement?
2. You may use software to do this problem. 3. The probability that a computer chip is defective is .0025. Find the probability that at most 30 of the next 10000 chips are defective (1) Using the binomial distribution. (2) Using the Poisson approximation to the binomial distribution. 3. Use Minitab to do this problem Fifty -five college students are interviewed about the quality of food in the college cafeteria. The probability that a student will reply that the quality of food is satisfactory is 0.37. A. What is the probability that exactly 25 students will reply that the quality of the food is satisfactory? B. What is the probability that at more than 20 students will reply that the quality of the food is satisfactory? C. What is the probability that between 25 and 30 students inclusive will reply that the quality of the food is unsatisfactory? See the Web page for an example. 6 Due 1/26 1. An article in the Journal of Structural Engineering suggests that yield strength of A36 grade steel is normally distributed with mean 43 and standard deviation 4.5 A. What is the probability (1) that the yield strength is at most 40? (2) that the yield strength is between 40 and 47.5? (3) that the yield strength is at least 50? B. What yield strength separates the strongest 75% from the others? 2. Do this problem using the software two ways. First use the normal approximation to the binomial distribution with the continuity correction. Then calculate the exact binomial probabilities. Compare the results. A safety engineer feels that 30% of all industrial accidents in her plant are caused by failure of employees to follow instructions. If this figure is correct what is the approximate and the exact probability that among 84 industrialized accidents in the plant anywhere from 22 to 28 inclusive will be due to failure of employees to follow instructions? 3. According to Motor Vehicle Facts and Figures published by the Motor Vehicle Manufacturers Association of the United States the mean age of cars in use is 7.4 years and the standard deviation is 2.6 years. Let x denote the mean age of a random sample of 100 cars. A. Determine the mean and the variance of x . B. Find P(x > 8) . C. Find the probability that the total age of 100 cars is at most 750 years.
7 Due 2/2 p.7 of 9 1. A certain metal is currently manufactured by a standard process. A new process has been developed in which an alloy has been added to the production of the metal. The manufacturers are interested in estimating the true difference between the mean breaking strength of the metals produced by the two processes. Twelve specimens of the metal are randomly selected from each of the two production methods and each specimen is subjected to stress until a crack is observed. The following are the breaking strengths of the specimens in kilograms per square centimeter.
Standard 428 419 458 439 441 456 463 429 438 445 441 463 process New 462 448 435 465 429 472 453 459 427 468 452 447 Process
Find a 95% confidence interval for each of the following. For each case give a careful statement of the assumptions. A. The mean breaking strength for the standard process. B. The mean breaking strength for the new process. C. The difference in the mean breaking strength between the standard process and the new process. D. The standard deviation of the mean breaking strength of both the standard process and the new process. E. The ratio of the standard deviations for the two processes. 2. You will need the computer to do this problem. No two students should get the same result. Suppose n = 64 men are selected at random from a large population. Assume the heights of the men in this population are normal with = 70 and = 5 4. Simulate the results of this selection 100 times and in each case find a 90% confidence interval for . A. How many of the intervals contain ? B. Would you expect all 100 of the intervals to contain ? Explain. C. Do all of the intervals have the same width? Why or why not? D. Suppose you took 85% intervals instead of 90%. Would they be narrower or wider? What about 95% intervals? E. How many intervals contain 71? 70? 69? F. Suppose you took samples of size 6400 instead of size 64. Would you expect more or fewer of the intervals to cover 71? 70? 69? Would these intervals be narrower or wider? G. Suppose you calculated 90% confidence intervals for 100 sets of real data. About how many of these intervals would you expect to contain ? Could you tell which intervals were successful and which were not? Why or why not? The following commands should generate the computer output. MTB > Random 64 c1-c100; SUBC> Normal 70 5. MTB > OneZ c1-c100; SUBC> Sigma 5; SUBC> Confidence 90.
8 Due 2/9 p.8 of 9 1. A. For Problem 1 Assignment 1 use Minitab to perform an appropriate test of hypothesis to determine whether the mean Octane rating of the gasoline is significantly greater than 85. Write a full report. Use =.05. Use the pull down menu under ...