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closer to campus. 33. 25 0 0 5 10 15 20 25 30 35 1134 Answers to Selected Exercises 35. Sample answer: the histogram is not as symmetric as the stem plot. The histogram more accurately shows the distribution of the data due to the smaller class interval of 5. Section 13.2, page 862 1. approximately 43.429 3. approxima...
gimel 0.45 hay 0.24 shin 0.21 Outcome 9. Answers may vary. Sample: 6 2 5 1 50 50 Probability 3 4 50 5 6 50 4 6 50 7 7 50 8 6 50 9 10 11 12 5 1 50 50 5 50 4 50 15. 0.0016 19. 2048 23. 362,880 27. 12,870 11. Answers may vary. Sample: 6.89 13. approximately 0.0027 17. 0.56; approximately 0.176 21. 3,268,760 25. approxima...
z-value 640 S 1.4 z-value 530 S 0.3 z-value $0.95 S 4.29 z-value $1.00 S 3.57 z-value $1.35 S 1.43 z-value 23. 0.48 25. 0.16 21. 0.19 27. 0.815 31. 63.25; Q3 Q1 fall between 63.25 and 76.75. 29. 0.48 76.75; Fifty percent of the scores Chapter 13 Review, page 900 1. qualitative 3. 25 20 15 10 5 sparrow purple finch chi...
2 9. A sample is shown of the program using the equation of the standard normal curve with a 3, h 0.5. close to the expected area of 0.997, or 99.7% of the area under the curve. The estimate is very b 3, and (Scales 84 X 192, 0.01 Y 0.05 ) 8. Samples of the program are shown for h 3; area 1.74 (Scales 3 x 3, 0.5 y 1 2...
to c, there are still an infinite number of both rational and irrational numbers between x and c, so t(x) will take the values 0 and 1 an infinite number of times, but never get close to a single number for all values of x that are very close to c. Section 14.2, page 923 1. 5 5. 0 13. 214 17. 1 2 3. Limit does not exi...
9. a. 1 b. 0 d. Limit does not exist. c. Limit does not exist. 11. a. 5 b. 0 c. 4 d. 2 13. 3 19. 2.5 15. 1 8 21. 2 17. Limit does not exist. 23. lim xS2 x 3 4 2 and lim xS2 3 x 4 1 Section 14.3, page 935 The symbol means β€œimplies.” 1 1. Given e 7 0, let Then 0 6. d e 3 x 3 0 3x 2 0 d e 6x 20 Then 6 e 0 6 0 x 5 0 Then ...
x2 2 2 lim xS3 1 5 2 lim xS3 lim xS3 1 x 2 x 2 1 22 7 3 1 2 x2 9 9. lim xS2 lim xS2 1 f 2 1 x lim xS2 1 lim xS2 1 x2 x 6 2 22 9 x2 x 6 x2 9 lim xS2 1 x2 6x 9 21 2 x2 6x 9 2 5 2 1 4 25 2 21 2 22 6 2 9 21 22 2 6 1 1 f 20 2 1 2 Answers to Selected Exercises 1139 f has a removable discontinuity at Chapter 14 Review, page ...
. 0 41. 0 1140 Answers to Selected Exercises 43. With a parachute: 20 ft/sec Without a parachute: 177.78 ft/sec 45. 1 47. 1 49. The first part of the informal definition is included in the second part, which says β€œthe values of f(x) can be made arbitrarily close to L by taking large enough values of x.” This means that...
1 2 1 21 2 5 Section A.2, page 976 c. less than 5 ft: less than 1 ft: Β’t 6 0.04902 sec. Β’t 6 0.0098 sec. 2. Lower estimate: 21 Upper estimate: 25 For the lower estimate, count all of the complete squares beneath the curve. For the upper estimate, count all of the complete squares below the curve and estimate the numbe...
2 x2 2xy y2 7 2 1 7y 21 2 2 2 23; 7 3 2 21 49xy then 7x 1 2 2 correct 1. 5. 9. 11. 17. 19. 23. 27. 31. 35. 39. 43. 47. 49. 53. 55. 65. 69. 73. 75. 77. 81. 3. 25. 29. 37. 33. 45. 41. 21. 8x x3 4x2 2x 3 7. 4z 12z2w 6z3w2 zw3 8 3x3 15x 8 13. 12a2x2 6a3xy 6a2xy 12z4 30z3 x2 x 2 y2 7y 12 3y3 9y2 4y 12 16a2 25b2 25x2 10bx b...
chosen. 95. Many correct answers Section A.3, page 981 21 21 9x 2 7 2z x 3 21 y 9 x 5 21 3x 1 21 1 x 8 9x 4u 3 x 5 x 2 2 x 5 2x y 21 x3 23 21 2u 3 21 x2 5x 25 2 3. 7. 11. 15. 19. 23. 27. 31. 35. 41. 45. 2 B x y 2 1 1 A 21 3y 5 2 15 x BA x y 3y 5 21 1 15 x x2 y2 21 z 1 z 3 21 x 3 2 x 9 21 2z 3 21 1 x 1 2 21 1 2x 5y x 2...
1 3 3 4x x 1 x 2 1 2 1 2 29. 2 31. 37. 43. 49. 55. 2 5y2 y 5 2 3 1 35 24 x2y2 x 2y x y 21 1 3y 3 y 2 2 3c 1 2 39. u 1 u 45. u2 v w 33. 3y x2 35. 41. 47. u v 21 1 2u v 21 1 x 3 2x 12x x 3 4u 3v 2 2u 3v 2 53. 59. y x xy xy x y 1 1 2 ; cd 51. 57 then 1 b a ab then 1 1 a b b 9, ; correct statement: 61. Example: if a 1, b ...
0, 0) is 2 by the midpoint and the distance from M to (0, r) is the same: B a b s2 4 r2 as is the distance from M to 1 s 2b a 2 s 2b r2 4 s2 4 2 2 s 2b r2 4 s2 49. Place one vertex of the rectangle at the origin, 11. 13. 15. 17. 4 1 βˆ’2 βˆ’4 1169.25 2, 2 has length 2 18. and Since 1 12 this is a right triangle. 110; 1 oth...
64 9. 3,921,225 x5 5x4y 10x3y2 10x2y3 5xy4 y5 a5 5a4b 10a3b2 10a2b3 5ab4 b5 32x5 80x4y2 80x3y4 40x2y6 10xy8 y10 x3 6x21x 15x2 20x1x 15x 61x 1 1 10c 45c2 120c3 210c6 120c7 12 4x 8 6x x 8i 45c8 10c9 4 4 x4 10x3y2 210c4 252c5 23. 56 29. 27. c10 35c3d4 11. 13. 15. 17. 19. 21. 25. 31. 37. a. b. 9 1b a n 1b a 9; 9! 1!8! n n...
12 1 b a x8h3 p x11 1144 Answers to Selected Exercises n r 3 1 21 47. a. x11 x2h9 a 12 11 b a xh10 h11 12 1 b when h is very close to 0 21 r 1 r 1 2 21 n r n r 12 10 b a 12x11, n r 1 n r 1 b. Since, n r! 2 n 1b n! n r n! 1 r 1 1 3 1 a r rb n. For example, rows 2 and 3 of Pascal’s triangle 1b are 1 1 2 1 3 3 1 that is,...
last parts of this equation say that the statement is true for n k 1. 1 2. Assume that the statement is true for k 1 12 22 32 p k2 k k 1 Add to both sides: 2 12 22 32 p k2 k 1 1 1 2 n k: 2k 1 21 2k 1 2 21 6 k 1 k k 1 1 21 2 2k 1 6 2k 1 6 2k2 7k 6 k 1 2 2 2k 3 2 21 2 3 21 21 The first and last parts of this equation sa...
1 3M 1 4M 1 factor of some integer M. Thus, 22k21 22 4 1. 3 1 1 this equation we see that k1 1 1. 22 3 2 1 n k 1. Therefore, the statement is true for 2 From the first and last terms of 2 22 22k1 3 1 222k1 4M 3 Hence, 3 is a factor of 12M 4 4M 1 k1 22 1 1 2 2. 1 2 1 1 17. Assume the statement is true for n k: 64 is a ...
p Proof: The statement is true for by part a. Assume that the statement is true for n k: xk yk x y xk1 xk2y p xy k2 y k1 yxk yxk 0 to write 21 1 Now use the fact that xk1 yk1 as follows: xk1 yk1 xk1 yxk yxk yk1 xk1 yxk x y x y 2 xk y 1 xk y 1 1 xk yk 2 xk1 xk2 y x y 21 xk3y2 p xyk2 yk1 yxk yk1 xk2y2 xk3y3 p xyk1 yk xk...
for all 22 7 2, Assume that n k: for k2 1 7 k 1. inequality show that the statement is true for n k 1. is true for all 34 81 and that the statement is true k2 2k 1 7 Therefore, by induction, the statement 24 10 4 16 40 56, The first and last terms of this k2 7 k. n 2. k 1 Then 2 2 1 we So the statement is true n 4. an...
moves needed to do this is one move to transfer the bottom ring [the k 1 st] from the first to the second peg. 1 Finally, the top k rings now on the third peg must be moved to the second peg. Once again by the induction hypothesis, the least number of moves for doing this is smallest total number of moves needed to k ...
34 between vectors, 671–673, 683 angle-side-angle (ASA) information, 631–632 Angle Theorem, 672 angular speed, 439–440 applications box construction, 103–104, 323 break-even point, 824 composition of functions, 195–196 compound interest, 345–349, 382, 402 distance, 101–102 exponential equations, 345–352, 379–384 food w...
585, 593–600, 604, 610 matrix, 804–805 vector, 657–659, 662, 683 adjacency matrix, 809–811 adjacent sides, 415 algebraic expressions, 973–977 amplitude, 494–497, 502–505, 516, 563 amplitude modulation (AM), 472, 499 analytic geometry, definition, 691 angle-angle-side (AAS) information, 626 Angle of Inclination Theorem,...
orations, 8, 16, 27, 201, 299, 409, 411, 457, 857, 861, 862, 877, 911, 994, 995, 1025 calculators absolute value, 110, 638 area under the normal curve, 895 complex numbers, 297, 299, 302–303, 638 composite functions, 193 conic sections, 721 continuity, 945 discontinuity, 115, 910, 937 dot mode, 157 ellipses, 695 factor...
76–79 instantaneous rates of change, 234–237, 614–615 limits of trigonometric functions, 566–568 maximum area of a triangle, 138–139 optimization applications, 322–324, 468–471 partial fractions, 838–841 Riemann sums, 964–967 tangents to exponential functions, 408–411 carbon-14 dating, 352, 381–382 cardioid graphs, 74...
conic sections definitions, 691, 747 degenerate, 691 discriminants, 723–724 eccentricity, 745–748 ellipses, 692–698, 716–722, 745–747, 767, 771–772 horizontal and vertical shifts, 716–717 hyperbolas, 700–706, 721–725, 745–750, 771–772 1150 Index identifying, 717–719, 722–723 nonstandard equations, 721–722 parabolas, 1...
593–595, 602–603, 611 exact values, 448–451, 536 graphs of, 475–478, 497–498 half-angle identities, 596–597, 611 inverse function, 532–534, 539–541, 563 law of, 617–622, 682 oscillating behavior, 568 periodicity, 456–458, 493–497, 516 phase shifts, 501–505, 516, 549 power-reducing identities, 595–596 product-to-sum id...
896 decomposition, partial fraction, 838–841 definite integrals, 967 degenerate conic sections, 691 degree measure, 94, 436–437, 462, 528 degree of a polynomial, 240–242, 260–261, 263, 313 DeMoivre’s Theorem, 644–645, 682 denominators, partial fractions, polynomial, 240–245 remainders and factors, 243–245 synthetic, 24...
349. see also exponential functions; logarithmic functions eccentricity, 745–748 effective rate of interest, 354 elementary row operations, 795–796 elevation, angles of, 425–429 eliminating the parameter, 757–759 elimination method, 783–786, 797–798, 821 ellipses applications, 696–698 characteristics, 694 circumference...
experiments binomial, 842, 884–888 definition, 864–865 probability estimates from, 874–877 Index 1151 exponential decay, 350–352, 402 exponential equations, 379–384 exponential functions. see also logarithmic functions applications, 345–352 bases, 336–337, 371, 380, 402 bases other than e, 410–411 common logarithms an...
free-fall, 958–959 frequency, definition, 844 frequency, wave, 558–562 frequency tables, 844–845 functions. see also logarithmic functions; polynomial functions; trigonometric functions absolute-value, 156, 173 composite, 193–195, 211–212, 944 concavity and inflection points, 154, 266 constant, 152, 173, 192, 953 cont...
ometric ratios, 443–444 vertical line test, 151–152, 225 zeros, 240, 245–248, 250–257, 265, 308–313, 316–317 Fundamental Counting Principle, 879–882, 899 Fundamental Theorem of Algebra, 307–313 Fundamental Theorem of Linear Programming, 829–831 G Gateway Arch (St. Louis, MO), 342 Gauss-Jordan elimination, 797–798, 252–...
283, 289 horizontal asymptotes, 284, 951–953 horizontal shifts, 175–176 horizontal stretches, 338–339 hyperbolas, 702–704 identifying, 505 identities, 506–507 increasing and decreasing functions, 152–154 inequalities, 121–123 inflection points, 154, 266 inverse cosine function, 533 inverse relations, 205–207 inverse si...
s formula, 633, 682 Hertz, 559 histograms, 849–850 holes, 282–283, 289, 910, 937–939 horizontal asymptotes, 284, 288, 951–953 horizontal lines, 37, 152, 792 horizontal line test, 209–210, 226, 530 horizontal shifts, 175–176 horizontal stretches and compressions, 178–180, 338–339 Hubble Space Telescope, 705 Huygens, Chr...
–945 interquartile range, 860–861 intersection method, 86, 127, 134, 524–525 interval notation, 118–119 interval of convergence, 520–521 inverse functions composition of, 532 cosine, 532–534, 538–539, 541, 563 definition, 210 horizontal line test, 530 restricting the domain, 210–211 sine, 529–532, 539, 563 tangent, 534...
954–957 trigonometric functions, 566–568 two-sided, 926–927 limits of sequences, 76–77 Limit Theorem, 922, 954 linear combinations of vectors, 662 linear depreciation, 35–36 linear equations, 33–37, 39 linear functions, 34–36, 240 linear inequalities, 119–120, 827 linear models corresponding function, 396 finite diffe...
800–801, 808–811 augmented, 795–798 dimensions, 804 directed networks, 809–811 elementary row operations, 795–796 equivalent, 795–796 Gauss-Jordan elimination, 797–798, 817 identity, 815 inverse, 815–817 matrix equations, 814, 817–818 multiplication, 805–809 notation, 299, 795, 797, 804 reduced row echelon form, 797–8...
330 n factorial, 520–521, 880 no correlation, 52 nonlinear systems, 779, 821–824 nonnegative integers, 3 nonrepeated linear factor denominators, 838–839 nonrepeated quadratic factor denominators, 838–839 nonsingular matrices, 815 normal curve area under, 906 definition, 889–890 empirical rule, 892–893, 899 equation of...
ms, 367, 915 outliers, 847, 862 output, 7, 9 P parabolas applications, 712–714 asymptotes, 286–287 characteristics, 711 curve fitting, 818 definitions, 163, 709, 747 equations, 712, 720, 770–771 graphs, 711–712 parameterization, 756–760, 769 polar equations, 749 translations, 719 parallel lines, 38–39, 66 parallel plan...
267, 316 graphs, 260–268 intercepts, 264–265, 267 limits of, 919–920 local extrema, 266–268 multiplicity, 265 points of inflection, 266, 317 polynomial inequalities, 127 polynomial models, 273–276 polynomials. see also polynomial functions bounds, 254–256 complex coefficients, 307–310 complex zeros, 309–313, 317 conju...
170 changing forms, 167–169 completing the square, 90–92 complex solutions, 298 definition, 88 discriminant, 93–94 quadratic equations (continued) rates of change factoring, 89 graphs of, 173 irreducible, 253 number of solutions, 93–94 parabolas, 163 polynomial form, 94–95, 164–167, 169, 225, 240 regression, 274–276 su...
, 444–445 radicals, 111–113, 327–329, 332– rectangles, 98–99, 703 rectangular box volume, 99–100, 333. see also roots radioactive decay, 340, 351–352, 402 radiocarbon dating, 352, 381–382 radio signals, 472, 500, 724–725 radio telescopes, 713–714 Ramanujan, 699 random samples, definition, 843 random variables, 869–870 ...
unity, 648–651, 682 rose graphs, 742 rotation angles, 730–731, 771 rotations, 722–723, 728–732, 771 rounding, 426, 525 rule of a relation, 7 rule of the function, 7 S samples, definition, 843 sample space, definition, 864–865 sample standard deviation, 858, 899 scalar multiplication, 655–656, 659, 661, 683, 805–806 sc...
497–498, 510–511 half-angle identities, 596–597, 604, 611 instantaneous rates of change, 614–615 inverse function, 529–532, 539, 563 1158 Index law of, 625–633, 682 oscillating behavior, 514–515 periodicity, 456–457, 493–494, 496–497, 516 phase shifts, 501–503, 516, 549 polar graphs, 740–741 power-reducing identities,...
39, 66 standard normal curve, 890, 893–896 standard position, of angles, 434 standard viewing window, 84 statistics. see also data box plots, 861–862 data displays, 844–850 five-number summary, 861–862 interquartile range, 860–861 mean, 853–854, 856–857, 869, 899 median, 854–856, 861 mode, 855–856, 898 range, 859–860 ...
, 563 periodicity, 456–457, 495, 516 restricted, 534 special angles, 418, 462 summary of properties, 483 trigonometric identities, 454–460, 463 two intersecting lines, 590–593 unit circle, 446 technology tips. see calculators telescopes, 705, 713–714 temperature, rate of change, 217–218 terminal points, of vectors, 653...
682 hypotenuses, 415 maximum area, 138–139 oblique, 617–622, 625–633 right, 414–419, 421–426 similar, 415–417 solving, 421–426 special, 418–419, 437, 462 standard notation, 617 trigonometric ratios, 415–417 Triangle Sum Theorem, 421 trigonometric equations algebraic solutions, 538–545 basic, 524–526, 538–542 complex n...
properties, 483, 490 trigonometric functions. see also transformations, 481–482, 487–489, 501–507, 446–449 unit circle, 446–449 trigonometric identities addition and subtraction, 581– 587, 593–600, 604, 610 Index 1159 trigonometric identities (continued) alternate solutions, 577–579 a sin x b cos x c, cofunction, 585–...
63 work calculation, 677–678 zero, 658 velocity average, 235 free-fall, 958–959 instantaneous, 234–236 terminal, 908, 959 total distance from, 964–965 vectors, 663 vertical asymptotes, 281–282, 288–289, 950 vertical lines, 37–38, 66, 792 vertical line test, 151–152, 186, 225 vertical shifts, 174, 481–482, 501, 504, 516...
313, 316–317 rational, 250–254, 316 of unity, 298–299 zero vectors, 658 z-values, 894–896, 900 Exponents crcs crs 2 crs cr c s s crs r crdr r cr dr 2 cr 1 cd 1 c db a Algebra Multiplication & Factoring Patterns Difference of Squares: Perfect Squares: Difference of Cubes: u2 v2 u v u v 1 21 2 2 u2 2uv v2 2 u2 2uv v2 2 2...
x1, y1) The equation of the straight line through The equation of line with slope m and y-intercept b is x1, y12 1 with slope m is y mx b. y y1 m x x12 1. Rectangular and Parametric Equations for Conic Sections h 1 x r cos t h y r sin t k Circle Center (h, k), radius r2 1 Ellipse Center (h, k) y k b2 1 2 2 2 x h a2 k k...
Β° 1 2 30Β° Law of Cosines a2 b2 c2 2bc cos A b2 a2 c2 2ac cos B c2 a2 b2 2ab cos C 3 A 60Β° 1 c U Degrees Radians sin U cos U tan U 0Β° 30Β° 45Β° 60Β° 90 12 2 13 2 1 1 13 2 12 2 1 2 0 0 13 3 1 13 undefined B b a C Law of Sines c a sin A b sin B sin C Area 1 2 ab sin C Heron’s Formula: Area 1s s a 1 21 s b 21 s c where Area F...
1 sin 1 x y sin 1 2 x y 22 sin x sin y 1 2 1 cos cos x cos y 1 2 1 cos x y x y 2 2 1 1 cos cos x y x y 1 1 22 22 cos x sin y 1 2 1 sin 1 x y sin 1 2 x y 22 sin x sin y 2 sin a sin x sin y 2 cos cos x cos y 2 cos cos x cos y 2 sin cos sin a a cos a sins as Ο€ 6, and so on. If you and your friends carry, Ο€, 3Ο€ 4, Ο€ 2, Ο€ ...
(32 ounces chocolate chip cookies). Name data sets that are quantitative discrete, quantitative continuous, and qualitative. Solution 1.7 One Possible Solution: β€’ The three cans of soup, two packages of nuts, four kinds of vegetables and two desserts are quantitative discrete data because you count them. This content ...
l are quantitative discrete; items d, j, and n are quantitative continuous; items b, c, g, h, i, and m are qualitative. 16 CHAPTER 1 | SAMPLING AND DATA 1.9 Determine the correct data type (quantitative or qualitative) for the number of cars in a parking lot. Indicate whether quantitative data are continuous or discre...
the data. There are no strict rules concerning which graphs to use. Two graphs that are used to display qualitative data are pie charts and bar graphs. In a pie chart, categories of data are represented by wedges in a circle and are proportional in size to the percent of individuals in each category. In a bar graph, t...
180 Native American 146 Pacific Islander 236 5,978 White TOTAL 36.1% 5.8% 5.3% 17.1% 0.6% 1.0% 24.5% 22,044 out of 24,382 90.4% out of 100% Table 1.4 Ethnicity of Students at De Anza College Fall Term 2007 (Census Day) Figure 1.8 20 CHAPTER 1 | SAMPLING AND DATA The following graph is the same as the previous graph but...
any other group of n individuals if the simple random sampling technique is used. In other words, each sample of the same size has an equal chance of being selected. For example, suppose Lisa wants to form a four-person study group (herself and three other people) from her pre-calculus class, which has 31 members not ...
, and Cuarismo. To generate random numbers: β€’ Press MATH. β€’ Arrow over to PRB. β€’ Press 5:randInt(. Enter 0, 30). β€’ Press ENTER for the first random number. β€’ Press ENTER two more times for the other 2 random numbers. If there is a repeat press ENTER again. Note: randInt(0, 30, 3) will generate 3 random numbers. Figure ...
a simple method. A type of sampling that is non-random is convenience sampling. Convenience sampling involves using results that are readily available. For example, a computer software store conducts a marketing study by interviewing potential customers This content is available for free at http://textbookequity.org/i...
decimal places. To four decimal places, these numbers are equivalent (0.0999). Sampling without replacement instead of sampling with replacement becomes a mathematical issue only when the population is small. For example, if the population is 25 people, the sample is ten, and you are sampling with replacement for any ...
to select 75 students. Each undergraduate student in the fall semester has the same probability of being chosen at any stage of the sampling process. 24 CHAPTER 1 | SAMPLING AND DATA d. The freshman, sophomore, junior, and senior years are numbered one, two, three, and four, respectively. A random number generator is ...
and enter 1, 60). This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 1 | SAMPLING AND DATA 25 β—¦ Press ENTER 15 times and record the numbers. β—¦ Record the quiz scores that correspond to these numbers. β—¦ These 15 quiz scores are the ...
the variability will begin to seem natural. Example 1.13 Suppose ABC College has 10,000 part-time students (the population). We are interested in the average amount of money a part-time student spends on books in the fall term. Asking all 10,000 students is an almost impossible task. Suppose we take two different samp...
ABC College are enrolled and that an equal number of part-time students are enrolled in each of the disciplines.) Each student is chosen using simple random sampling. Using a calculator, random numbers are generated and a student from a particular discipline is selected if he or she has a corresponding number. The stu...
in the cluster. 4. To determine the proportion of people taking public transportation to work, survey 20 people in New York City. Conduct the survey by sitting in Central Park on a bench and interviewing every person who sits next to you. 5. To determine the average cost of a two-day stay in a hospital in Massachusett...
samples cannot be stressed enough. Size of a Sample The size of a sample (often called the number of observations) is important. The examples you have seen in this book so far have been small. Samples of only a few hundred observations, or even smaller, are sufficient for many purposes. In polling, samples that are fr...
the response β€’ Non-response or refusal of subject to participate: The collected responses may no longer be representative of the population. Often, people with strong positive or negative opinions may answer surveys, which can affect the results. β€’ Causality: A relationship between two variables does not mean that one...
Not every statistical operation can be used with every set of data. Data can be classified into four levels of measurement. They are (from lowest to highest level): β€’ Nominal scale level β€’ Ordinal scale level β€’ Interval scale level β€’ Ratio scale level Data that is measured using a nominal scale is qualitative. Categor...
is 80Β° F four times as hot as 20Β° F). There is no meaning to the ratio of 80 to 20 (or four to one). Data that is measured using the ratio scale takes care of the ratio problem and gives you the most information. Ratio scale data is like interval scale data, but it has a 0 point and ratios can be calculated. For examp...
. Cumulative relative frequency is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row, as shown in Table 1.11. This content is available for free at http://textbookequity.org/introduc...
92 + 0.07 = 0.99 0.99 + 0.01 = 1.00 Total = 100 Total = 1.00 Table 1.12 Frequency Table of Soccer Player Height 32 CHAPTER 1 | SAMPLING AND DATA The data in this table have been grouped into the following intervals: β€’ 59.95 to 61.95 inches β€’ 61.95 to 63.95 inches β€’ 63.95 to 65.95 inches β€’ 65.95 to 67.95 inches β€’ 67.95 ...
0.18 6 50 7 50 15 50 8 50 9 50 0.12 0.12 + 0.14 = 0.26 0.26 + 0.30 = 0.56 0.56 + 0.16 = 0.72 0.72 + 0.18 = 0.90 This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 1 | SAMPLING AND DATA 33 Rainfall (Inches) Frequency Relative Freque...
CHAPTER 1 | SAMPLING AND DATA 1.16 From Table 1.13, find the number of towns that have rainfall between 2.95 and 9.01 inches. In your class, have someone conduct a survey of the number of siblings (brothers and sisters) each student has. Create a frequency table. Add to it a relative frequency column and a cumulative ...
1579, 0.2105, 0.3684, 0.4737, 0.6316, 0.7368, 0.7895, 0.8421, 0.9474, 1.0000. c. d. 5 19 7 19, 12 19, 7 19 1.17 Table 1.13 represents the amount, in inches, of annual rainfall in a sample of towns. What fraction of towns surveyed get between 11.03 and 13.05 inches of rainfall each year? Example 1.18 Table 1.15 contains...
What is the frequency of deaths measured from 2000 through 2004? b. What percentage of deaths occurred after 2006? c. What is the relative frequency of deaths that occurred in 2000 or before? d. What is the percentage of deaths that occurred in 2011? e. What is the cumulative relative frequency for 2006? Explain what ...
the potential lurking variables are spread equally among the groups. At this point the only difference between groups is the one imposed by the researcher. Different outcomes measured in the response variable, therefore, must be a direct result of the different treatments. In this way, an experiment can prove a cause-...
will!”: placebo effects of an ergogenic aid on athletic performance. Journal of Sport & Exercise Psychology. 2007 Jun. 29(3):382-94. Web. April 30, 2013. 38 CHAPTER 1 | SAMPLING AND DATA The experimental units are the individual men in the study. The explanatory variable is oral medication. The treatments are aspirin ...
of drivers while texting and while driving only. How many seconds does it take for a driver to respond when a leading car hits the brakes? a. Describe the explanatory and response variables in the study. b. What are the treatments? c. What should you consider when selecting participants? d. Your research partner wants...
in existing datasets, β€’ changing measuring instruments without reporting the change, and β€’ misrepresenting the number of experimental subjects. Clearly, it is never acceptable to falsify data the way this researcher did. Sometimes, however, violations of ethics are not as easy to spot. Researchers have a responsibilit...
The Mind of a Con Man,” Magazine, New York Times, April 26, 2013. Available online at: http://www.nytimes.com/2013/04/28/magazine/diederik-stapels-audacious-academic-fraud.html?src=dayp&_r=2& (accessed May 1, 2013). 3. β€œFlawed Science: The Fraudulent Research Practices of Social Psychologist Diederik Stapel,” Tillburg ...
selecting a convenient sample, the researcher is intentionally selecting a sample that could be biased. Claiming that this sample represents the community is misleading. The researcher needs to select areas in the community at random. b. c. Intentionally omitting relevant data will create bias in the sample. Suppose t...
to the start of the list. For each marked name record the five data values. You now have a total of 60 data values. 3. For each name marked, record the data. ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ______ ...
. __________ 4. __________ 9. __________ 14. __________ 5. __________ 10. __________ 15. __________ Table 1.21 A Systematic Sample Pick a systematic sample of 15 restaurants. 1. Describe your procedure. 2. Complete the table with your sample. 1. __________ 6. __________ 11. __________ 2. __________ 7. __________ 12. __...
24 A Cluster Sample Pick a cluster sample of restaurants from two cities. The number of restaurants will vary. 1. Describe your procedure. 2. Complete the table with your sample. 1. ________ 6. ________ 11. ________ 16. ________ 21. ________ 2. ________ 7. ________ 12. ________ 17. ________ 22. ________ 3. ________ 8. ...
Unit any individual or object to be measured Explanatory Variable the independent variable in an experiment; the value controlled by researchers Frequency the number of times a value of the data occurs Informed Consent Any human subject in a research study must be cognizant of any risks or costs associated with the st...
with Replacement Once a member of the population is selected for inclusion in a sample, that member is returned to the population for the selection of the next individual. Sampling without Replacement A member of the population may be chosen for inclusion in a sample only once. If chosen, the member is not returned to...
population. When properly selected, larger samples model the population more closely than smaller samples. There are many different potential problems that can affect the reliability of a sample. Statistical data needs to be critically analyzed, not simply accepted. 1.3 Frequency, Frequency Tables, and Levels of Measu...
post guidelines for proper conduct. It is important that you learn basic statistical procedures so that you can recognize proper data analysis. PRACTICE 1.1 Definitions of Statistics, Probability, and Key Terms Use the following information to answer the next five exercises. Studies are often done by pharmaceutical co...
number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas. The first house in the neighborhood around the park was selected randomly, and then the resident of every eighth house in the neighborhood around the park was interviewed. 7. The sampling method was a. si...
new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once starting the treatment. Two researchers each follow a different set of 40 AIDS patients from the start of treatment unt...
How might the researchers gather random data? 22. Suppose that the first researcher conducted his survey by randomly choosing one state in the nation and then randomly picking 40 patients from that state. What sampling method would that researcher have used? 23. Suppose that the second researcher conducted his survey ...
study collected the data in Table 1.31. The second study collected the data in Table 1.32. 52 CHAPTER 1 | SAMPLING AND DATA Group Showed improvement No improvement Deterioration Used program 142 Did not use program 72 Table 1.31 43 110 15 18 Group Showed improvement No improvement Deterioration Used program 105 Did no...
year-old women l. Common letter grades: A, B, C, D, and F 1.4 Experimental Design and Ethics 40. Design an experiment. Identify the explanatory and response variables. Describe the population being studied and the experimental units. Explain the treatments that will be used and how they will be assigned to the experim...
Community College math students are absent from class during a quarter. 50. What is the population she is interested in? a. all Lake Tahoe Community College students b. all Lake Tahoe Community College English students c. all Lake Tahoe Community College students in her classes d. all Lake Tahoe Community College math...
with the way the survey was conducted. b. Using complete sentences, list three ways that you would improve the survey if it were to be repeated. 66. Suppose you want to determine the mean number of students per statistics class in your state. Describe a possible sampling method in three to five complete sentences. Mak...
whether books are checked out by an adult or a child. She records this data for every fourth patron who checks out books. e. A political party wants to know the reaction of voters to a debate between the candidates. The day after the debate, the party’s polling staff calls 1,200 randomly selected phone numbers. If a r...
. a. Do you have any health problems that prevent you from doing any of the things people your age can normally do? b. During the past 30 days, for about how many days did poor health keep you from doing your usual activities? c. d. Do you have health insurance coverage? In the last seven days, on how many days did you...
the validity of estimates drawn from such research.”[6] The Pew Research Center for People and the Press admits: β€œThe percentage of people we interview – out of all we try to interview – has been declining over the past decade or more.”[7] 5. lastbaldeagle. 2013. On Tax Day, House to Call for Firing Federal Workers Wh...
, to the nearest year, they have lived in the U.S. The data are as follows: 2; 5; 7; 2; 2; 10; 20; 15; 0; 7; 0; 20; 5; 12; 15; 12; 4; 5; 10. Table 1.35 was produced. Data Frequency Relative Frequency Cumulative Relative Frequency 0 2 4 2 3 1 2 19 3 19 1 19 0.1053 0.2632 0.3158 Table 1.35 Frequency of Immigrant Survey R...
9 18.9 27.5 17.9 21.8 20.9 16.7 27.3 18.2 24.7 20.0 22.6 23.9 18.0 31.4 22.3 24.0 25.5 24.7 24.6 28.1 24.9 22.6 23.6 23.4 25.7 24.8 25.5 21.2 25.7 23.1 23.0 23.9 26.0 16.3 23.1 21.4 21.5 27.0 27.0 18.6 31.7 23.3 30.1 22.9 23.3 21.7 18.6 Table 1.36 84. Forbes magazine published data on the best small firms in 2012. Thes...