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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition

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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 1 preview image’SSOLUTIONSMANUALJAMESLAPPAPATHWAY TOINTRODUCTORYSTATISTICSSECONDEDITIONJay LehmannCollege of San Mateo
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 2 preview image
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 3 preview imageTable of ContentsChapter 1: Performing Operations and Evaluating Expressions1.1Variables, Constants, Plotting Points, and Inequalities ................................................................ 11.2Expressions................................................................................................................................... 41.3Operations with Fractions and Proportions; Converting Units..................................................... 71.4Absolute Value and Adding Real Numbers................................................................................ 111.5Change in a Quantity and Subtracting Real Numbers ................................................................ 141.6Ratios, Percents, and Multiplying and Dividing Real Numbers................................................. 161.7Exponents, Square Roots, Order of Operations, and Scientific Notation ................................... 20Review Exercises ....................................................................................................................... 24Chapter Test ............................................................................................................................... 27Chapter 2: Designing Observational Studies and Experiments2.1Simple Random Sampling .......................................................................................................... 312.2Systematic, Stratified, and Cluster Sampling ............................................................................. 342.3Observational Studies and Experiments ..................................................................................... 36Review Exercises ....................................................................................................................... 40Chapter Test ............................................................................................................................... 43Chapter 3: Graphical and Tabular Displays of Data3.1Frequency Tables, Relative Frequency Tables, and Bar Graphs ................................................ 453.2Pie Charts and Two-Way Tables ................................................................................................ 493.3Dotplots, Stemplots, and Time-Series Plots ............................................................................... 523.4Histograms.................................................................................................................................. 583.5Misleading Graphical Displays of Data...................................................................................... 64Review Exercises ....................................................................................................................... 66Chapter Test ............................................................................................................................... 71Chapter 4: Summarizing Data Numerically4.1Measures of Center..................................................................................................................... 754.2Measures of Spread .................................................................................................................... 804.3Boxplots ..................................................................................................................................... 85Review Exercises ....................................................................................................................... 90Chapter Test ............................................................................................................................... 92Chapter 5: Computing Probabilities5.1Meaning of Probability............................................................................................................... 955.2Complement and Addition Rules ............................................................................................... 975.3Conditional Probability and the Multiplication Rule for Independent Events.......................... 1005.4Discrete Random Variables...................................................................................................... 1035.5Finding Probabilities for a Normal Distribution....................................................................... 1065.6Finding Values of Variables for Normal Distributions ............................................................ 110Review Exercises ..................................................................................................................... 112Chapter Test ............................................................................................................................. 114Chapter 6: Describing Associations of Two Variables Graphically6.1Scatterplots ............................................................................................................................... 1176.2Determining the Four Characteristics of an Association .......................................................... 1216.3Modeling Linear Associations.................................................................................................. 125Review Exercises ..................................................................................................................... 130Chapter Test ............................................................................................................................. 133
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 4 preview imageChapter 7: Graphing Equations of Lines and Linear Models; Rate of Change7.1Graphing Equations of Lines and Linear Models..................................................................... 1357.2Rate of Change and Slope of a Line ......................................................................................... 1387.3Using Slope to Graph Equations of Lines and Linear Models ................................................. 1427.4Functions .................................................................................................................................. 148Review Exercises ..................................................................................................................... 152Chapter Test ............................................................................................................................. 156Chapter 8: Solving Linear Equations and Inequalities to Make Prediction8.1Simplifying Expressions........................................................................................................... 1598.2Solving Linear Equations in One Variable............................................................................... 1618.3Solving Linear Equations to Make Predictions ........................................................................ 1638.4Solving Formulas ..................................................................................................................... 1708.5Solving Linear Inequalities to Make Predictions...................................................................... 175Review Exercises ..................................................................................................................... 181Chapter Test ............................................................................................................................. 186Chapter 9: Finding Equations of Linear Models9.1Using Two Points to Find an Equation of a Line ..................................................................... 1919.2Using Two Points to Find an Equation of a Linear Model ....................................................... 1939.3Linear Regression Model ......................................................................................................... 198Review Exercises ..................................................................................................................... 204Chapter Test ............................................................................................................................. 207Chapter 10: Using Exponential Models to Make Predictions10.1Integer Exponents..................................................................................................................... 20910.2Rational Exponents................................................................................................................... 21110.3Graphing Exponential Models.................................................................................................. 21310.4Using Two Points to Find an Equation of an Exponential Model ............................................ 21610.5Exponential Regression Model................................................................................................. 221Review Exercises ..................................................................................................................... 226Chapter Test ............................................................................................................................. 230
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 5 preview imageChapter 1: Performing Operations and Evaluating Expressions1Chapter 1: Performing Operations and Evaluating ExpressionsHomework 1.12. A constant is a symbol that represents a specific number.4. Data are quantities or categories that describe people, animals, or things.6. In 2017, about 37% of children aged 6–12 participated in a team sport (organized or unorganized) on a regularbasis.8. The temperature is10 F. That is, the temperature is 10 degrees below 0 (in Fahrenheit).10. The statement3t represents the year 2012 (3 years before 2015).12. Answers may vary. Example: Letsbe the annual salary (in thousands of dollars) of a person. Thenscanrepresent the numbers 25 and 32, butscannot represent the numbers15and9.14. Answers may vary. Example: Letnbe the number of students enrolled in a prestatistics class. Thenncanrepresent the numbers 15 and 28, butncannot represent the numbers20or 0.5.16. Answers may vary. Example: LetTbe the temperature (in degrees Fahrenheit) in an oven. ThenTcanrepresent the numbers 300 and 450, butTcannot represent the numbers300or450.18.a.Answers may vary. Some possible answers are shown below.b.In the described situation, the symbolsWandLare variables. Their values can change.c.In the described situation, the symbolAis a constant. Its value is fixed at 36 square feet.20.a.Answers may vary. Some possible answers are shown below.b.In the described situation, the symbolsW,L, andAare all variables. All their values can change.c.In the described situation, none of the symbols are constants. All their values can change.22.24.26.28. The counting numbers between 1 and 5 are 2, 3,and 4.30. The integers between6and 3, inclusive, are6,5,4,3,2,1,0, 1, 2, and 3.32.34. The positive integers between4and 4 are 1,2, and 3.36. Answers may vary. Example:2,5and40.38. Answers may vary. Example:2.1,2.3,and2.8.40. The temperature at the top of a skyscraper can be positive or negative, depending on the location of theskyscraper and the time of year. Temperature is not usually reported using fractions. So, among the choices,the integers are the smallest group of number that contains possible data.
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 6 preview image2ISM: A Pathway to Introductory Statistics42. The commute time of an employee cannot be negative, but it can be measured in fractions. So, among thechoices, the nonnegative real numbers are the smallest group of numbers that contains possible data.44. McDonald’s sells hamburgers every day of every year and there is never just a portion of a hamburger sold. So,among the choices, the counting numbers is the smallest group of numbers that contains possible data.46.48.50.52.a.b.The number of hours of video uploaded to YouTube per minute increased between 2009 and 2014. Thenumber of hours of video uploaded to YouTube per minute went up each year.c.The annualincreasesin the number of hours of video uploaded to YouTube per minute increased between2009 and 2014. The annual increases are shown below.YearsIncrease2009 to 20102514112010 to 20114825232011 to 20127348252012 to 201310073272013 to 201430010020054.a.b.The number of microbreweries increased from 2013 to 2017.c.The increases in the number of microbreweries stayed approximately constant from 2013 to 2017. Theannual increases are shown below.YearsIncrease2013 to 20142.11.50.62014 to 20152.62.10.52015 to 20163.22.60.62016 to 20173.83.20.656. – 68.70. They-coordinate is4.
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 7 preview imageChapter 1: Performing Operations and Evaluating Expressions372. Point A is 2 units to the left of the origin and 4 units down. Thus, its coordinates are( 2,4).Point B is 3 units to the left of the origin on thex-axis. Thus, its coordinates are( 3, 0).Point C is 5 units to the left of the origin and 4 units up. Thus, its coordinates are( 5, 4).Point D is 4 units to the right of the origin and 2 units up. Thus, its coordinates are(4, 2).Point E is 3 units below the origin on they-axis. Thus, its coordinates are(0,3).Point F is 3 units to the right of the origin and 2 units down. Thus, its coordinates are(3,2).74. True. The number2lies to the right of6on a number line.76. False.55 , thus5is not strictly greater than5.78.80.82.84.86. Inequality:5x Interval notation:5,Graph:88. Inequality:3xInterval notation:,3Graph:90. Inequality:1x Interval notation:1,Graph:92.In WordsInequalityGraphIntervalNotationnumbers less thanor equal to66x ,6 numbers greater than 11x1,numbers greater than orequal to44x 4,numbers less than 55x(,5)94.96.98.100.In WordsInequalityGraphInterval Notationnumbers between–3 and 030x( 3, 0)numbers between1 and 4, as well as 114x[1, 4)numbers between–3 and 1, as well as 131x( 3,1]numbers between–4 and –1, inclusive41x [ 4,1]
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 8 preview image4ISM: A Pathway to Introductory Statistics102. The student completes the homework assignment in 30 or more minutes.104. Inequality:44hInterval notation:44,Graph:106. Inequality:2TInterval notation:, 2Graph:108. Inequality:4.2VInterval notation:4.2,Graph:110. The average gas mileage of a car on highwaysis between 35 and 40 miles per gallon.112. Inequality:4156TInterval notation:41,56Graph:114. Inequality:140145wInterval notation:(140,145)Graph:116. No. Answers may vary. Example: The numbers 2 and 5 are not “between 2 and 5.” The integers between 2 and5 are simply 3 and 4.118. The ordered pairs selected and plotted points may vary. The points will lie on the same horizontal line.Answers may vary.120. Answers may vary. The inequality represents “4 is less than or equal to 4,” and 4 is equal to 4.122. The types of numbers discussed in this section are real numbers, rational number, irrational numbers, integers,and counting numbers (or natural numbers). Answers may vary.Homework 1.22. We evaluate an expression by substituting a number for each variable in the expression and then calculating theresult.4. The quotient ofaandbisa/b, wherebis not zero.6. Substitute 6 forxin5x:56118. Substitute 6 forxin4x:64210. Substitute 6 forxin(9)x:695412. Substitute 6 forxin30x:30(6)514. Substitute 6 forxinxx:66016. Substitute 6 forxinxx:66118. Substitute 47 forrin29r:472976. So, if 47% of Republicans favor gays to marry legally in 2017,then in that same year, about 76% of Democrats favor gays to marry legally.20. Substitute 13.5 forUin6U:13.567.5. So, in 2016 if the average daily shipping volume for UPS was13.5 million packages, in that same year, the average daily shipping volume for FedEx was about 7.5 millionpackages.22. Substitute 17 fornin599.99n:599.99 1710,199.83. So, if 17 thousand Fender Standard Jazz Electric BassGuitars with maple fingerboards are sold, the total revenue is about $10,200,000.24. Substitute 328 forTin4T:328482. So, if a student earns a total of 328 points on four tests, thestudent’s average test score is 82 points.
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 9 preview imageChapter 1: Performing Operations and Evaluating Expressions526.a.Speed LimitDriving Speed(miles per hour)(miles per hour)353554040545455505055ssThe expression5srepresents the driving speed if the speed limit issmiles per hour.b.Substitute 65 forsin5s:65570. So, if the speed limit is 65 miles per hour, the person will bedriving 70 miles per hour.28.a.Number of SharesTotal Value(dollars)174.74 1274.74 2374.74 3474.74 474.74nnThe expression74.74nrepresents the total value of the shares.b.Substitute 7 fornin74.74n:74.74 7523.18. So, the total value of 7 shares is $523.18.30.a.Number of SiblingsShare of Cost(dollars)2300023300034300045300053000nnThe expression3000nrepresents each sibling’s share of the cost in dollars.b.Substitute 6 fornin3000n:30006500. So, the share of each sibling’s cost is $500.32.a.We can write an expression10vto represent the total cost of parking and money spent on a vase.b.Substitute 25 forvin the expression10v:102535. So, if $10 is spent on parking then the total costof parking and money spent on a vase is $35.34.a.We can write an expression2rto represent the net price of a shaver whose retail price isrdollars.b.Substitute 6 forrin the expression2r:624. So, if the retail price of a shaver is $6, then the netprice is $4.36.a.We can write an expression105cto represent the total cost of tuition when enrolling inccredits ofclasses.b.Substitute 15 forcin the expression105c:105 151575. So, if a student enrolls in 15 credits of classes,then the total cost of tuition is $1575.38.a.We can write an expression420nto represent the equal share each ofnsiblings will receive of theinheritance.b.Substitute 3 fornin the expression420n:4203140. So, each of 3 siblings will receive an equalshare of $140,000 of a $420,000 inheritance.
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 10 preview image6ISM: A Pathway to Introductory Statistics40.8x; substitute 8 forxin8x:880.42.6x; substitute 8 forxin6x:6814.44.15;xsubstitute 8 forxin15:x(8)1523.46.7x; substitute 8 forxin7x:871.48.5x; substitute 8 forxin5x:5 840.50. The quotient of 6 and the number52. Two less than the number54. The sum of 4 and the number56. The product of the number and 558. The sum of the number and 360. The quotient of the number and 562. Substitute 6 forxand 3 foryin the expressionyx:36964. Substitute 6 forxand 3 foryin the expressionxy:6318.66. Substitute 6 forxand 3 foryin the expressionxy:632.68.xy; substitute 9 forxand 3 foryin the expressionxy:9312.70.xy; substitute 9 forxand 3 foryin the expressionxy:933.72. Substitute 90.0 forcand 104.8 forrin the expressioncr:90.0104.8194.8.So, in 2015 the averageannual per-person consumption of chicken and red meat was 194.8 pounds.74. Substitute 11.26 forwand 19.98 forain the expressionaw:19.9811.268.72.So, in 2015 the collegeenrollments of all students who were not women was 8.72 million.76. Substitute 2.5 forNand 1.8 forAin the expressionNA:2.5 1.84.5.So, in 2016 the average number of APexams taken was 4.5 million.78. Substitute 205,200 forsand 3.6 fornin the expressionsn: 205, 2003.657, 000.So, in 2014 the averagemoney earned by a teacher was about $57,000.80.a.Substitute 4 forxin the expression2x:426.Substitute 5 forxin the expression2x:527. Substitute 6 forxin the expression2x:628.b.Substitute 4 forxin the expression2 :x2 48. Substitute 5 forxin the expression2x:2 510.Substitute 6 forxin the expression2 :x2 612.c.Observe the values after substitution are different for the two expressions.2244262(4)855272(5)1066282(6)12xxx82.a.313 1323 2633 3943 412nnThe price of bread is $3, $6, $9, and $12 for 1, 2, 3, and 4 loaves, respectively.b.The cost per loaf of bread is $3. The cost per loaf is a constant while the number of loaves is a variable. Inthe expression3 ,nthe constant is 3 and the variable isn.c.Answers may vary. Example: For each additional loaf bought, the total price increases by $3.
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 11 preview imageChapter 1: Performing Operations and Evaluating Expressions784.a.212 1222 2432 3642 48ttThe elevator rises are 2 yards, 4 yards, 6 yards, and 8 yards for every 1, 2, 3, and 4 seconds, respectively.b.The elevator is rising at a speed of 2 yards per second. The distance risen is a constant amount of 2 yardswhile the number of seconds is a variable. In the expression2 ,tthe constant is 2 and the variable ist.c.Answers may vary. Example: For each second that passes, the distance the elevator rises is another 2yards.86. Answers may vary.88. Answers may vary.Homework 1.32. The reciprocal ofabis.ba4. If an object is made up of two or more parts, then the sum of their proportions equals 1.6. The numerator of25is 2.8.182 923 32 3 310.244 62 22 32 2 2 312.273 933 33 3 314.1055 2153 73 5 716.102 5255142 727718.273 3 33 3 311543 3 3 23 3 32220.93 33 3111813 3 3 33 3 3 33 3922.153 53555183 3 23 3 23 2624.545 45 2 220797 97 3 36326.252 52 555363 63 2 33 3928.5525 2552121212 2 32 3630.72737 312312212 27 3772 2 3 22 2 2832.48434 32 2 33373787 87 2 2 27 21434.4414 12 22229929 23 3 23 3936.2828102 52151515153 5338.13913942 222181818182 3 33 3940. The LCD is 9:15135358393 3999942. The LCD is 24:313 314948683642424132444. The LCD is 7:3273143172717777746. The LCD is 4:313123214242244448. The LCD is 42:54574635246767764242114250. The LCD is 7:91 79792171 7777727 
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 12 preview image8ISM: A Pathway to Introductory Statistics52.337351547454728554.55205215 3 773203213203 2 2 542156.2525152535 5 35915939153 3 3 59358. Substitute 3 forxand 12 forzin the expressionzx:123 2 22 24433 11160. Substitute 4 forw, 3 forx, 5 fory, and 12 forzin the expressionywzx:545 2 2551232 2 3 33 3962. Substitute 3 forx, 5 fory, and 12 forzin the expressionyyxz:55312The LCD is 12:5554520525312341212121264.673810.9071 39966.149311.162155268.6143911.8570140070. Answers may vary. Example:72. In 2018, since 10 of the top 40 songs sold on iTunes were pop songs, we can write a proportion of the songsthat were pop songs as101404.74. The whole survey group consists of the proportions of the three political parties, so the sum of the proportionsequals 1.
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 13 preview imageChapter 1: Performing Operations and Evaluating Expressions976. The category of American adults who picked football as their favorite sport to watch OR who pickedbasketball as their favorite sport to watch is the category of adult Americans who picked football together withthe adults who picked basketball. So, we add the fractions41119.41491 1111911 99 1136119999479978. Proportion of employees who spend at least $101 on commuting to work:1175125735353580. Proportion of the disk that is orange:27251777782. Proportion of Hispanic adults that do not use at least one social media site:81183111111111.84. Proportion of the disc that is red and blue:1132523666Proportion of the disc that is yellow:56511666686. Proportion of Hispanic and Caucasian undergraduates:21471172141414.Proportion of undergraduates of ethnicities other than Hispanic and Caucasian:1114113114141414.88. Letmbe the proportion of income for mortgage andfbe the proportion of income for food. The proportionremaining is given by the expression1mf. Substitute13formand16forfin the expression.1111361 61211 632662166662163612mfSo,12of the income remains.
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 14 preview image10ISM: A Pathway to Introductory Statistics90.a.i.2370 out of 3180 degrees were bachelor’s degrees. Proportion of bachelor’s degrees:23700.7453180.ii.23703180237081010.2553180318031803180iii. 496 + 84 = 580 degrees were master’s and doctoral degrees. Proportion of master’s and doctoraldegrees:5800.1823180.b.The six exact proportions consist of all the degrees the university awards, so the sum of the exactproportions equals 1. This may not be the case for the sum of the approximations. Rounding may cause thesum to differ slightly from 1.92.23 centimeters1 inch9.06 inches12.54 centimeters94.113 kilometers1 mile70.19 miles per hour1 hour1.61 kilometers96.42.5 milligrams1 gram16 ounces0.68 grams = 0.68 grams per pound1 ounce1000 milligrams1 pound1 pound98.25 meters3600 seconds1 kilometer1 mile55.90 miles per hour1 second1 hour1000 meters 1.61 kilometers100.2250 milligrams1 gram16 ounces = 3.6 grams per pound10 ounces1000 milligrams1 pound102.126, 000cupmilligrams26 grams 1000 milligrams883250 milligrams per ounce1 cup1 gram1 ounce1 ounce104. Answers may vary. Example: In this case, Student 2 actually did better. When you compare the proportion ofquestion right for Student 1,824110050with the proportion of question right for Student 2,4350, we see thatStudent 2 did better since43415050.106.a.i.232 361323 26ii.474 7281747 428iii.161 661616 16b.Answers may vary. Example: The product of a fraction and its reciprocal equals 1.108. Answers may vary. Example: The student should have only multiplied the numerator by 2. Rewrite 2 as21andthen multiply across.3232 362 5151 55110. Answers may vary. Example: The denominator of a fraction is the name of the things it represents. Thenumerator of a fraction is the number of those things it represents. When we add two fractions with the samedenominator, we keep the same denominator, or name, and add the two numerators, or number of things.
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 15 preview imageChapter 1: Performing Operations and Evaluating Expressions11Homework 1.42. The absolute value of a number is the distance the number is from 0 on the number line.4. False. The sum of –4 and 2 is negative:422 . The sum of 5 and –1 is positive:5( 1)4 .6.99 8.222    10.66because 6 is a distance of 6 units from 0 on a number line.12.11because1is a distance of 1 unit from 0 on a number line.14.555  16.999   18. The numbers have different signs, so subtract the smaller absolute value from the larger.53532 Since5is greater than3, the sum is positive.532 20. The numbers have the same sign, so add the absolute values.32325 The numbers are negative, so the sum is negative.325  22. The numbers have different signs, so subtract the smaller absolute value from the larger.96963Since9is greater than6, the sum is negative.693  24. The numbers have different signs, so subtract the smaller absolute value from the larger.43431 Since4is greater than3, the sum is positive.34126. The numbers have the same sign, so add the absolute values.959514 The numbers are negative, so the sum is negative.9514  28. The numbers have different signs, so subtract the smaller absolute value from the larger.82826 Since8is greater than2, the sum is positive.826 30.880 because the numbers are opposites and the sum of opposites is 0.32.770because the numbers are opposites and the sum of opposites is 0.34. The numbers have different signs, so subtract the smaller absolute value from the larger.171417143 Since17is greater than14, the sum is positive.17143 
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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition - Page 16 preview image12ISM: A Pathway to Introductory Statistics36. The numbers have different signs, so subtract the smaller absolute value from the larger.8957895732Since89is greater than57, the sum is negative.895732 38. The numbers have the same sign, so add the absolute values.347594347594941 The numbers are negative, so the sum is negative.347594941  40.127,512127,5120 because the numbers are opposites and the sum of opposites is 0.42. The numbers have the same sign, so add the absolute values.3.79.93.79.913.6 The numbers are negative, so the sum is negative.3.79.913.6  44. The numbers have different signs, so subtract the smaller absolute value from the larger.70.370.36.7 Since7is greater than0.3, the sum is positive.0.376.746. The numbers have different signs, so subtract the smaller absolute value from the larger.37.0519.2637.0519.2617.79 Since37.05is greater than19.26, the sum is positive.37.0519.2617.79 48. The numbers have different signs, so subtract the smaller absolute value from the larger.2121155555 Since25is greater than15, the sum is positive.21155550. The numbers have different signs, so subtract the smaller absolute value from the larger.515142666663Since56is greater than16, the sum is negative.512663 52. The numbers have the same sign, so add the absolute values.2525225459336363266662 The numbers are negative, so the sum is negative.253362 
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