Skip to content
Textbook Guides

Solution Manual for Introduction to Probability and Statistics, 15th Edition

Solution Manual for Introduction to Probability and Statistics, 15th Edition is your study companion, providing answers to textbook exercises and reinforcing key concepts.

Preview 16 of 505 pages

See the first 16 pages exactly as they appear in the document.

  1. Page 1
    Read page 1 as text

    Complete Solutions Manual to Accompany Introduction to Probability and Statistics 15th Edition William Mendenhall, III 1925-2009 Robert J. Beaver University of California, Riverside, Emeritus Prepared by Barbara M. Beaver Barbara M. Beaver University of California, Riverside, Emerita

  2. Page 2
  3. Page 3
    Read page 3 as text

    Contents Chapter 1: Describing Data with Graphs………………………………………………………...1 Chapter 2: Describing Data with Numerical Measures………………………………………....30 Chapter 3: Describing Bivariate Data……………………………………………………..........68 Chapter 4: Probability…………………………………………………………………..............93 Chapter 5: Discrete Probability Distribution…………………………………………………..121 Chapter 6: The Normal Probability Distribution……………………………………………...156 Chapter 7: Sampling Distributions…………………………………………………………….186 Chapter 8: Large-Sample Estimation………………………………………………………….210 Chapter 9: Large-Sample Test of Hypotheses………………………………………………...240 Chapter 10: Inference from Small Samples…………………………………………………...271 Chapter 11: The Analysis of Variance………………………………………………………...324 Chapter 12: Linear Regression and Correlation……………………………………………….364 Chapter 13: Multiple Regression Analysis……………………………………………………415 Chapter 14: The Analysis of Categorical Data..........................................................................439 Chapter 15: Nonparametric Statistics………………………………………………………….469

  4. Page 4
    Read page 4 as text

    1 1: Describing Data with Graphs Section 1.1 1.1 .1 The experimental unit, the individual or object on which a variable is measured, is the student. 1.1.2 The experimental unit on which the number of errors is measured is the exam. 1.1. 3 The experimental unit is the patient. 1.1.4 The experimental unit is the azalea plant. 1.1.5 The experimental unit is the car. 1. 1.6 “Time to assemble” is a quantitative variable because a numerical quantity (1 hour, 1.5 hours, etc.) is measured. 1.1.7 “Number of students” is a quantitative variable because a numerical quantity (1, 2, etc.) is measured. 1.1.8 “Rating of a politician” is a qualitative variable since a quality (excellent, good, fair, poor) is measured. 1.1.9 “State of residence” is a qualitative variable sinc e a quality (CA, MT, AL, etc.) is measured. 1. 1.10 “Population” is a discrete variable because it can take on only integer values. 1.1.11 “Weight” is a continuous variable, taking on any values associated with an interval on the real line. 1.1.12 Number of claims is a discrete variable because it can take on only integer values. 1.1.13 “Number of consumers” is integer - valued and hence discrete . 1.1.14 “Number of boating accidents” is integer - valued and hence discrete . 1.1.15 “Time” is a continuous variable. 1.1.16 “Cost of a head of lettuce” is a discrete variable since money can be measured only in dollars and cents . 1.1.17 “Number of brothers and sisters” is integer - valued and hence discrete . 1.1.18 “Yield in bushels ” is a continuous variable, tak ing on any values associated with an interval on the real line. 1.1.19 The statewide database contains a record of all drivers in the state of Michigan. The data collected represents the population of interest to the researcher. 1.1.20 The researcher is in terested in the opinions of all citizens, not just the 1000 citizens that have been interviewed. The responses of these 1000 citizens represent a sample . 1.1.21 The researcher is interested in the weight gain of all animals that might be put on this diet, not just the twenty animals that have been observed. The responses of these twenty animals is a sample . 1.1.22 The data from the Internal Revenue Service contain s the records of all wage earners in the United States. The data collected represents the population of interest to the researcher. 1.1.23 a The experimental unit, the item or object on which variables are measured, is the vehicle. b Type (qualitative); m ake (qualitative); carpool or not? (qualitative); one - way commute distance (quantitative continuous); age of vehicle (quantitative continuous) c Since five variables have been measured, th is is multivariate data. 1.1.24 a The set of ages at death represen ts a population, because there have only been 3 8 different presidents in the United States history. b The variable being measured is the continuous variable “age”. c “Age” is a quantitative variable.

  5. Page 5
    Read page 5 as text

    2 1.1.25 a The population of interest consists of voter opinions (for or against the candidate) at the time of the election for all persons voting in the election. b Note that when a sample is taken (at some time prior or the election), we are not actually sampling from the population of interest. As time pa sses, voter opinions change. Hence, the population of voter opinions changes with time, and the sample may not be representative of the population of interest. 1.1.26 a - b The variable “survival time” is a quantitative continuous variable. c The populatio n of interest is the population of survival times for all patients having a particular type of cancer and having undergone a particular type of radiotherapy. d - e Note that there is a problem with sampling in this situation. If we sample from all patients having cancer and radiotherapy, some may still be living and their survival time will not be measurable. Hence, we cannot sample directly from the population of interest, but must arrive at some reasonable alternate population from which to sample. 1.1.2 7 a The variable “reading score” is a quantitative variable, which is probably integer - valued and hence discrete. b The individual on which the variable is measured is the student. c The population is hypothetical – it does not exist in fact – but consists of the reading scores for all students who could possibly be taught by this method. Section 1. 2 1.2.1 The pie chart is constructed by partitioning the circle into five parts, according to the total contributed by each part. Since the total number of students is 100, the total number receiving a final grade of A represents 31 100 0.31 = or 31% of the total. Thus, this category will be represented by a sector angle of 0.31(360) 111.6 =  . The other sector angles are shown next , along with the pie chart. Final Grade Frequency Fraction of Total Sector Angle A 31 .31 111.6 B 36 .36 129.6 C 21 .21 75.6 D 9 .09 32.4 F 3 .03 10.8 3 . 0 % F 9 . 0 % D 2 1 . 0 % C 3 6 . 0 % B 3 1 . 0 % A

  6. Page 6
    Read page 6 as text

    3 The bar chart represents each category as a bar with height equal to the frequency of occurrence of that category and is shown in the figure that follows . 1. 2.2 Construct a statistical table to summarize the data. The pie and bar charts are shown in the figures that follow . Status Frequency Fraction of Total Sector Angle Freshman 32 .32 115.2 Sophomore 34 .34 122.4 Junior 17 .17 61.2 Senior 9 .09 32.4 Grad Student 8 .08 28.8 1.2.3 Construct a statistical table to summarize the data. The pie and bar charts are shown in the figures that follow . Status Frequency Fraction of Total Sector Angle Humanities, Arts & Sciences 43 .43 154.8 Natural/Agricultural Sciences 32 .32 115.2 Business 17 .17 61.2 Other 8 .08 28.8 F D C B A 4 0 3 0 2 0 1 0 0 F i n a l G r a d e F r e q u e n c y 8 . 0 % G r a d S t u d e n t 9 . 0 % S e n i o r 1 7 . 0 % J u n i o r 3 4 . 0 % S o p h o m o r e 3 2 . 0 % F r e s h m a n G r a d S t u d e n t S e n i o r J u n i o r S o p h o m o r e F r e s h m a n 3 5 3 0 2 5 2 0 1 5 1 0 5 0 S t a t u s F r e q u e n c y

  7. Page 7
    Read page 7 as text

    4 1.2.4 a The pie chart is constructed by partitioning the circle into four parts, according to the total contributed by each part. Since the total number of people is 50, the total number in category A represents 11 50 0.22 = or 22% of the total. Thus, this category will be represented by a sector angle of o 0.22(360) 79.2 = . The other sector angles are shown below. The pie chart is shown in the figure that follows . Category Frequency Fraction of Total Sector Angle A 11 .22 79.2 B 14 .28 100.8 C 20 .40 144.0 D 5 .10 36.0 b The bar chart represents each category as a bar with height equal to the frequency of occurrence of that category and is shown in the figure above . c Yes, the shape will change depending on the order of presentation. The order is unimportant. d The proportion of people in categories B, C, or D is found by summing the frequencies in those three categories, and dividing by n = 50. That is, ( ) 14 20 5 50 0.78 + + = . e Since there are 14 people in category B, there are 50 14 36 − = who are not, and the percentage is calculated as ( ) 36 50 100 72% = . 1. 2.5 a - b Construct a statistical table to summarize the data. The pie and bar charts are shown in th e figures that follow . 8 . 0 % o t h e r 1 7 . 0 % B u s i n e s s 3 2 . 0 % N a t u r a l / A g r i c u l t u r a l S c i e n c e s 4 3 . 0 % H u m a n i t i e s , A r t s & S c i e n c e s O t h e r B u s i n e s s N a t u r a l / A g r i c u l t u r a l S c i e n c e s H u m a n i t i e s , A r t s & S c i e n c e s 4 0 3 0 2 0 1 0 0 C o l l e g e F r e q u e n c y 1 0 . 0 % D 4 0 . 0 % C 2 8 . 0 % B 2 2 . 0 % A D C B A 2 0 1 5 1 0 5 0 C a t e g o r y F r e q u e n c y

  8. Page 8
    Read page 8 as text

    5 State Frequency Fraction of Total Sector Angle CA 9 .36 129.6 AZ 8 .32 115.2 TX 8 .32 115.2 c From the table or the chart, Texas produced 8 25 0.32 = of the jeans. d The highest bar represents California, which produced the most pairs of jeans. e Since the bars and the sectors are almost equal in size, the three states produced roughly the same number of pairs of jeans. 1.2.6 - 9 The bar charts represent each category as a bar with height equal to the frequency of occurrence of that category. 1.2.10 Answers will vary. 1. 2.11 a The percentages given in the exercise only add to 94%. We should add another category called “Other”, which will account for the oth er 6% of the responses. b Either type of chart is appropriate. Since the data is already presented as percentages of the whole group, we choose to use a pie chart, shown in the figure that follows . 3 2 . 0 % T X 3 2 . 0 % A Z 3 6 . 0 % C A T X A Z C A 9 8 7 6 5 4 3 2 1 0 S t a t e F r e q u e n c y D e m o c r a t s I n d e p e n d e n t s R e p u b l i c a n s 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 0 P a r t y I D P e r c e n t E x e r c i s e 6 5 5 + 3 5 t o 5 4 1 8 t o 3 4 7 0 6 0 5 0 4 0 3 0 2 0 1 0 0 A g e P e r c e n t E x e r c i s e 7 D e m o c r a t s I n d e p e n d e n t s R e p u b l i c a n s 1 0 0 8 0 6 0 4 0 2 0 0 P a r t y I D P e r c e n t E x e r c i s e 8 5 5 + 3 5 t o 5 4 1 8 t o 3 4 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 0 A g e P e r c e n t E x e r c i s e 9

  9. Page 9
    Read page 9 as text

    6 c - d Answers will vary. 1. 2 .12 - 14 The percentages falling in each of the four categories in 2017 are shown next (in parentheses) , and the pie chart for 2017 and bar charts for 2010 and 2017 follow . Region 2010 2017 United States/Canada 99 183 (13.8%) Europe 107 271 (20.4%) Asia 64 453 (34.2%) Rest of the World 58 419 (31.6%) Total 328 1326 (100%) 6 . 0 % o t h e r 5 . 0 % T o o m u c h a r g u i n g 1 4 . 0 % N o t g o o d a t i t 1 5 . 0 % T o o m u c h w o r k 2 0 . 0 % T o o m u c h p r e s s u r e 4 0 . 0 % O t h e r p l a n s 3 1 . 6 % R e s t o f t h e W o r l d 3 4 . 2 % A s i a 2 0 . 4 % E u r o p e 1 3 . 8 % U . S . / C a n a d a E x e r c i s e 1 2 ( 2 0 1 7 ) R e s t o f t h e W o r l d A s i a E u r o p e U . S . / C a n a d a 1 2 0 1 0 0 8 0 6 0 4 0 2 0 0 R e g i o n A v e r a g e D a i l y U s e r s ( m i l l i o n s ) E x e r c i s e 1 3 ( 2 0 1 0 ) R e s t o f t h e W o r l d A s i a E u r o p e U . S . / C a n a d a 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 0 R e g i o n A v e r a g e D a i l y U s e r s ( m i l l i o n s ) E x e r c i s e 1 4 ( 2 0 1 7 )

  10. Page 10
    Read page 10 as text

    7 1.2.15 Users in Asia and the rest of the world have increased more rapidly than those in the U.S., Canada or Europe over the seven - year period. 1.2.16 a The total percentage of responses given in the table is only (40 34 19)% 93% + + = . Hence there are 7% of the opinions not recorded, which should go into a category called “Other” or “More than a few days”. b Yes. The bars are very close to the correct proportions. c Similar to previous exercises. The pie chart is shown next . The bar chart is probably more interesting to look at. 1.2.17 - 18 Answers will vary from student to student. Since the graph gives a range of values for Zimbabwe’s share, we h ave chosen to use the 13% figure, and have used 3% in the “Other” category. The pie chart and bar charts are shown next . 1.2.19 - 20 The Pareto chart is shown below. The Pareto chart is more effective than the bar chart or the pie chart . 1.2.21 The data should be displayed with either a bar chart or a pie chart. The pie chart is shown next . 7 . 0 % M o r t h a n a F e w D a y s 1 9 . 0 % N o T i m e 3 4 . 0 % A F e w D a y s 4 0 . 0 % O n e D a y 3 . 0 % o t h e r 2 0 . 0 % R u s s i a 1 8 . 0 % C a n a d a 1 0 . 0 % S o u t h A f r i c a 1 0 . 0 % A n g o l a 1 3 . 0 % Z i m b a b w e 2 6 . 0 % B o t s w a n a O t h e r R u s s i a C a n a d a S o u t h A f r i c a A n g o l a Z i m b a b w e B o t s w a n a 2 5 2 0 1 5 1 0 5 0 C o u n t r y P e r c e n t S h a r e O t h e r S o u t h A f r i c a A n g o l a Z i m b a b w e C a n a d a R u s s i a B o t s w a n a 2 5 2 0 1 5 1 0 5 0 C o u n t r y P e r c e n t S h a r e

  11. Page 11
    Read page 11 as text

    8 Section 1. 3 1.3.1 The dotplot is shown next ; the data is skewed right, with one outlier , x = 2.0 . 1.3.2 The dotplot is shown next ; the data is relatively mound - shaped, with no outliers. 1. 3.3 - 5 The most obvious choice of a stem is to use the ones digit. The portion of the observation to the right of the ones digit constitutes the leaf. Observations are classified by row according to stem a nd also within each stem according to relative magnitude. The stem and leaf display is shown next . 1 6 8 2 1 2 5 5 5 7 8 8 9 9 3 1 1 4 5 5 6 6 6 7 7 7 7 8 9 9 9 leaf digit = 0.1 4 0 0 0 1 2 2 3 4 5 6 7 8 9 9 9 1 2 represents 1.2 5 1 1 6 6 7 6 1 2 3. The stem and leaf display has a mound shaped distribution , with no outliers . 4. From the stem and leaf display, the smallest observation is 1.6 (1 6). 5. The eight and ninth largest observations are both 4.9 (4 9). 1 . 0 % o t h e r 1 . 0 % G r e e n 2 . 0 % Y e l l o w / G o l d 4 . 0 % B e i g e / B r o w n 2 0 . 8 % W h i t e / W h i t e p e a r l 1 0 . 9 % R e d 8 . 9 % B l u e 1 6 . 8 % G r a y 2 0 . 8 % B l a c k / B l a c k e f f e c t 1 3 . 9 % S i l v e r 2 . 0 1 . 8 1 . 6 1 . 4 1 . 2 1 . 0 E x e r c i s e 1 6 2 6 0 5 8 5 6 5 4 E x e r c i s e 2

  12. Page 12
    Read page 12 as text

    9 1.3.6 The stem is chosen as the ones digit, and the portion of the observation to the right of the ones digit is the leaf. 3 | 2 3 4 5 5 5 6 6 7 9 9 9 9 4 | 0 0 2 2 3 3 3 4 4 5 8 leaf digit = 0.1 1 2 represents 1.2 1.3.7 - 8 The stems are split, with the leaf digits 0 to 4 belonging to the first part of the stem and the leaf digits 5 to 9 belonging to the second. The stem and leaf display shown below improves the presentation of the data. 3 | 2 3 4 3 | 5 5 5 6 6 7 9 9 9 9 leaf digit = 0.1 1 2 represents 1.2 4 | 0 0 2 2 3 3 3 4 4 4 | 5 8 1. 3.9 The scale is drawn on the horizontal axis and the measurements are represented by dots. 1.3.10 Since there is only one digit in each measurement, the ones digit must be the stem, and the leaf will be a zero digit for each measurement. 0 | 0 0 0 0 0 1 | 0 0 0 0 0 0 0 0 0 2 | 0 0 0 0 0 0 1.3.11 The distribution is relatively mound - shaped, with no outliers. 1.3.12 The two plots convey the same information if the stem and leaf plot is turned 90 o and stretched to resemble the dotplot. 1.3.13 The line chart plots “day” on the horizontal axis and “time” on the vertica l axis. The line chart shown next reveals that learning is taking place, since the time decreases each successive day. 1.3.14 The line graph is shown next . Notice the change in y as x increases. The measurements are decreasing over time. 2 1 0 E x e r c i s e 9 5 4 3 2 1 4 5 4 0 3 5 3 0 2 5 D a y T i m e ( s e c o n d s )

  13. Page 13
    Read page 13 as text

    10 1.3.15 The dotplot is shown next . a The distribution is somewhat mound - shaped (as much as a small set can be); there are no outliers. b 2 10 0.2 = 1 .3.16 a The test scores are graphed using a stem and leaf plot generated by Minitab . b - c The distribution is not mound - shaped, but is rather has two peaks centered around the scores 65 and 85. This might indicate that the students are divided into two groups – those who understand the material and do well on exams, and those who do not have a thorough command of the material. 1.3 .17 a We choose a stem and leaf plot, using the ones and tenths place as the stem, and a zero digit as the leaf. The Minitab printout is shown next. 1 0 8 6 4 2 0 6 3 6 2 6 1 6 0 5 9 5 8 5 7 5 6 Y e a r M e a s u r e m e n t 7 6 5 4 3 2 1 Number of Cheeseburgers

  14. Page 14
    Read page 14 as text

    11 b The data set is relatively mound - shaped, centered at 5.2. c The value 5.7 x = does not fall within the range of the other cell counts, and would be considered somewhat unusual. 1.3.18 a - b The dotplot and the stem and leaf plot are drawn using Minitab . c The measurements all seem to be within the same range of variability. There do not appear to be any outliers. 1.3.19 a Stem and leaf displays may vary from student to student. The most obvious choice is to use the tens digit as the stem and the ones digit as the leaf. 7 | 8 9 8 | 0 1 7 9 | 0 1 2 4 4 5 6 6 6 8 8 10 | 1 7 9 11 | 2 b The display is fairly mound - shaped, with a large peak in the middle. 1.3.20 a The sizes and volumes of the food items do increase as the number of calories increase, but not in the correct proportion to the actual calories. The differences in calorie content are not accurately portrayed in the graph. b The bar graph which accurately portrays the number of calories in the six food item s is shown next . 2.82 2.80 2.78 2.76 2.74 2.72 2.70 2.68 Calcium Dotplot of Calcium

  15. Page 15
    Read page 15 as text

    12 1 .3.21 a - b The bar charts for the median weekly earnings and unemployment rates for eight different levels of education are shown next . c The unemployment rate drops and the median weekly earnings rise as the level of educational attainment increases. 1.3.22 a Similar to previous exercises. The pie chart is shown next . b The bar chart is shown next . W h o p p e r P i z z a 1 2 o z B e e r 1 2 o z C o k e O r e o H e r s h e y ' s K i s s 9 0 0 8 0 0 7 0 0 6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 0 F o o d I t e m N u m b e r o f C a l o r i e s L e s s t h a n h i g h s c h o o l d i p l o m a H i g h s c h o o l d i p l o m a S o m e c o l l e g e , n o d e g r e e A s s o c i a t e ' s d e g r e e B a c h e l o r ' s d e g r e e M a s t e r ' s d e g r e e P r o f e s s i o n a l d e g r e e D o c t o r a l d e g r e e 8 7 6 5 4 3 2 1 0 E d u c a t i o n a l A t t a i n m e n t U n e m p l o y m e n t r a t e L e s s t h a n h i g h s c h o o l d i p l o m a H i g h s c h o o l d i p l o m a S o m e c o l l e g e , n o d e g r e e A s s o c i a t e ' s d e g r e e B a c h e l o r ' s d e g r e e M a s t e r ' s d e g r e e P r o f e s s i o n a l d e g r e e D o c t o r a l d e g r e e 2 0 0 0 1 5 0 0 1 0 0 0 5 0 0 0 E d u c a t i o n a l A t t a i n m e n t M e d i a n w k l y e a r n i n g s 1 . 1 % o t h e r 6 . 8 % C h i n e s e T r a d i t i o n a l 0 . 4 % S i k h i s m 0 . 2 % J u d a i s m 6 . 9 % P r i m a l I n d i g e n o u s & A f r i c a n T r a d i t i o n a l 2 6 . 0 % I s l a m 1 5 . 6 % H i n d u i s m 3 6 . 4 % C h r i s t i a n i t y 6 . 5 % B u d d h i s m

  16. Page 16
    Read page 16 as text

    13 c The Pareto chart is a bar chart with the heights of the bars ordered from large to small. This display is more effective than the pie chart. 1. 3.23 a The distribution is skewed to the right, with a several unusually large measurements. The five state s marked as HI are California, New Jersey, New York and Pennsylvania. b Three of the four states are quite large in area, which might explain the large number of hazardous waste sites. However, New Jersey is relatively small, and other large states do no t have unusually large number of waste sites. The pattern is not clear. 1.3.24 a The distribution is skewed to the right, with two outliers. b The dotplot is shown next . It conveys nearly the same information, but the stem - and - leaf plot may be more i nformative. O t h e r C h i n e s e T r a d i t i o n a l S i k h i s m J u d a i s m P r i m a l I n d i g e n o u s & A f r i c a n T r a d i t i o n a l I s l a m H i n d u i s m C h r i s t i a n i t y B u d d h i s m 2 0 0 0 1 5 0 0 1 0 0 0 5 0 0 0 R e l i g i o n M e m b e r s ( m i l l i o n s ) J u d a i s m S i k h i s m O t h e r B u d d h i s m C h i n e s e T r a d i t i o n a l P r i m a l I n d i g e n o u s & A f r i c a n T r a d i t i o n a l H i n d u i s m I s l a m C h r i s t i a n i t y 2 0 0 0 1 5 0 0 1 0 0 0 5 0 0 0 R e l i g i o n M e m b e r s ( m i l l i o n s )

489 more pages in the full document

Unlock it once and it stays in your library, ready to chat with or turn into flashcards.

Unlock the full document

More Statistics study materials

See all

Study this document with CramX

Once it is in your library, every tool can work from it.