Solution manual for statistics for science and engineering by kinney

Solution Manual for Statistics for Science and Engineering by Kinney Full file at https://TestbankDirect.eu/ CHAPTER SOLUTIONS TO EXERCISES Chapter One Exercises 1.1 b) Sample A is considerably more variable than Sample B and Sample A appears to be centered about a larger value than Sample B ( A = 476, sA = 379.36, B = 398, sB = 154.69.) Students can later compute these sample means and standard deviations to verify these conclusions c) Gears of type A appear to last longer, but those of type B would be more reliable b) A is the least variable while B is the most variable These conclusions are easily seen in the dotplots Means and standard deviations in order A, B, C are : 24.7, 25.1, 23.94, 0.678, 3.30, 1.861 Students normally will not compute these numbers at this stage c) I’d choose A since its mean value is not much less than B’s (which is larger), but A has the smallest standard deviation, so it is more reliable than the others Section 1.2 The object of this section is to show some problems that are to come in the book The three examples here illustrate some of the most important scientific and engineering applications of statistics Although there are no exercises in this section, it is interesting to allow students to explore the data sets in their own way At this point one gets graphical analyses almost exclusively, but occasionally students will explore programs in Minitab or some other statistical program for which they are unprepared Conclusions can also be drawn, foreshadowing hypothesis testing and estimation It is useful to set students up for what is to come; then the topics appear to be far less arbitrary than they might appear if suddenly sprung on the student Instructors may wish to use data sets illustrating other statistical topics they will cover in the course Topics that can be used include a fractional factorial experiment, multiple regression, or a quality control chart for a data set less well behaved than that given in this section Exercises 1.3 a) The 28 samples that can be drawn are {(1, 2), (1, 3), , (7, 8)} These should all be enumerated b) The histogram of the population is flat with height for each of the values 1, 2, , c) There are 13 different values for the means : 3/2, 2, 5/2, , 15/2, which appear with frequencies 1, 1, 2, 2, 3, 3, 4, 3, 3, 2, 2, 1, d) The ranges take on the integer values from to and have frequencies taking on the integer values from to This produces a steadily decreasing histogram The midpoints of the bars could be joined by a straight line which is easily computed The most frequent range is since that occurs for the samples (1, 2), (2, 3), (3, 4), Full file at https://TestbankDirect.eu/ Solution Manual for Statistics for Science and Engineering by Kinney Full file at https://TestbankDirect.eu/ CHAPTER SOLUTIONS TO EXERCISES (4, 5), (5, 6), (6, 7)and (7, 8) It is also easy in this case to enumerate the samples with other values for the range When this is done, one can see why the histogram for the range differs markedly from that for the sample means Exercises 1.4 a) Minitab boxplots show for Year 1, Q1 = 35, Q2 = 57.5 and Q3 = 72.75 and the boxplot for Year gives Q1 = 42.75, Q2 = 53.5 and Q3 = 59.75 showing that the data for Year is less variable than that for Year b) Stem-and-leaf plots convey the same information as the boxplots a) Stem-and-leaf of Trans N = 15 Leaf Unit = 0.10 00 0000 (3) 000 000 00 50 b) The boxplot shows Q1 = 1, Q2 = and Q3 = 3 a) For the midpoint values {0, 1, 2, 3, 4, 5, 6, 7} the histogram shows frequencies of {6, 5, 5, 3, 1, 3, 6, 1} b) The boxplot shows a range of about units and has no outliers a) Stem-and-leaf of Vol N = 14 Leaf Unit = 10 149 50 67 559 71 5589 34 b) Minitab gives the following values: Q1 = 575.0, Q2 = 705.5 and Q3 = 788.7 Minitab gives the following character histogram: Histogram of Time N = 20 Midpoint Count Full file at https://TestbankDirect.eu/ Solution Manual for Statistics for Science and Engineering by Kinney Full file at https://TestbankDirect.eu/ CHAPTER SOLUTIONS TO EXERCISES 21.0 * 21.5 *** 22.0 ** 22.5 **** 23.0 ** 23.5 ** 24.0 * 24.5 ** 25.0 * 25.5 * a) Stem-and-leaf of Life N = 19 Leaf Unit = 1.0 12 66 74 88 9 678 (4) 10 0123 10 699 11 24 11 12 00 b) Minitab gives the following values: Q1 = 88, Q2 = 101 and Q3 = 109 There are no outliers c) The data are fairly disperse and show a long left-hand tail a) The quartiles are 5, 8, and 10 b) The observation 23 is an outlier a) A is the most consistent, but this worker also produces brakewheels that are farthest from the target value b) A a) The quartiles are 90, 100, and 111 Full file at https://TestbankDirect.eu/ Solution Manual for Statistics for Science and Engineering by Kinney Full file at https://TestbankDirect.eu/ CHAPTER SOLUTIONS TO EXERCISES b) Outliers are data points less than 90 − 1.5(111 − 90) = 58 or data points greater than 111 + 1.5(111 − 90) = 142 There are no values in either of these ranges 10 a) The quartiles are at 36,500, 68,500 and 105,000 miles b) Outliers would then be values less than 36,500-1.5(105,000-36,500) = - 66,250 miles or values greater than 105,000 + 1.5(105,000-36,500) = 207,750 miles There no such observations 11 a) The quartiles appear to be at 4, 9, and 13 approximately b) It appears that a little less than 60% of the data is below the median and the remaining 40% of the data is above the median c) The graph should show a long right-hand tail Exercises 1.5 a) x = 72.315, s = 14.8302 b) Chebyshev’s Inequality indicates that some of the data is in the interval In fact, 13/20 = 65% of the data is in the interval a) x = 5.760, s = 6.8592 b) x = 5.760/150 = 0.0 384, s = 6.8592/(25)2 = 0.010975 a) x = 70.85, s = 262.1161 b) The interval (x − 2s, x + 2s) is the interval (38.47, 103.23) which contains all the observations Chebyshev’s Inequality indicates that at least 3/4 of the data is in this interval a) x = 2.0060, s = 0.0111 b) The interval (x −1.5s, x +1.5s) is the interval (1.8478, 2.1643) which contains or 80% of the data Chebychev’s Inequality indicates that at least − 1/((1.5)ˆ2) = 56% of the data are in this interval a) x = 16.67, s = 15.8404 b) k = since this interval contains all the data except for the points 9, 21, and 22 Full file at https://TestbankDirect.eu/ .. .Solution Manual for Statistics for Science and Engineering by Kinney Full file at https://TestbankDirect.eu/ CHAPTER SOLUTIONS TO EXERCISES (4, 5), (5, 6), (6, 7 )and (7, 8) It is... are 90, 100, and 111 Full file at https://TestbankDirect.eu/ Solution Manual for Statistics for Science and Engineering by Kinney Full file at https://TestbankDirect.eu/ CHAPTER SOLUTIONS TO... Full file at https://TestbankDirect.eu/ Solution Manual for Statistics for Science and Engineering by Kinney Full file at https://TestbankDirect.eu/ CHAPTER SOLUTIONS TO EXERCISES 21.0 * 21.5 ***