Chapter 3 Extra Practice
3.1 Introduction to Bivariate Data
1. The following figure shows a random sample of 100 hikers and the areas of hiking they prefer.
Sex  The coastline  Near lakes and streams  One mountain peaks  Total 

Female  18  16  ___  45 
Male  ___  ___  14  55 
Total  ___  41  ___  ___ 
Figure 3.26
 Complete the table.
 Are the events “being female” and “preferring the coastline” independent events?Let F = being female, and let C = preferring the coastline.
 Find P(F AND C).
 Find P(F)P(C)
Are these two numbers the same? If they are, then F and C are independent. If they are not, then F and C are not independent.

Find the probability that a person is male, given that the person prefers hiking near lakes and streams. Let M = being male, and let L = preferring hiking near lakes and streams.
 What word tells you this is a conditional?
 Fill in the blanks, and calculate the probability: P(  ) = .
 Is the sample space for this problem all 100 hikers? If not, what is it?

Find the probability that a person is female or prefers hiking on mountain peaks. Let F = being female, and let P = preferring mountain peaks.
 Find P(F).
 Find P(P).
 Find P(F AND P).
 Find P(F OR P).
Solution:

Sex The coastline Near lakes and streams One mountain peaks Total Female 18 16 11 45 Male 16 25 14 55 Total 34 41 25 100 Figure 3.27

 P(F AND C) = = 0.18
 P(F)P(C) = = (0.45)(0.34) = 0.153
 P(F AND C) ≠ P(F)P(C), so the events F and C are not independent.

 The word “given” tells you that this is a conditional.
 P(ML) =
 No, the sample space for this problem is the 41 hikers who prefer lakes and streams.

 P(F) =
 P(P) =
 P(F AND P) =
 P(F OR P) = + – =
2. The figure below shows a random sample of 200 cyclists and the routes they prefer. Let M = males and H = hilly path.
Gender  Lake path  Hilly path  Wooded path  Total 

Female  45  38  27  110 
Male  26  52  12  90 
Total  71  90  39  200 
Figure 3.28
 Out of the males, what is the probability that the cyclist prefers a hilly path?
 Are the events “being male” and “preferring the hilly path” independent events?
3. Muddy Mouse lives in a cage with three doors. If Muddy goes out the first door, the probability that he gets caught by Alissa the Cat is and the probability he is not caught is . If he goes out the second door, the probability he gets caught by Alissa is and the probability he is not caught is . The probability that Alissa catches Muddy coming out of the third door is , and the probability she does not catch Muddy is . It is equally likely that Muddy will choose any of the three doors, so the probability of choosing each door is .
Caught or not  Door 1  Door 2  Door 3  Total 

Caught  
Not caught  
Total  1 
Figure 3.29
 The first entry is P(Door 1 AND Caught)
 The entry is P(Door 1 AND Not Caught)
Verify the remaining entries.
 Complete the probability contingency table. Calculate the entries for the totals. Verify that the lowerright corner entry is 1.
 What is the probability that Alissa does not catch Muddy?
 What is the probability that Muddy chooses Door 1 OR Door 2, given that Muddy is caught by Alissa?
Solution:

Caught or not Door 1 Door 2 Door 3 Total Caught Not caught Total 1 Figure 3.30
4. The figure below relates the weights and heights of a group of individuals participating in an observational study.
Weight/height  Tall  Medium  Short  Total 

Obsese  18  28  14  
Normal  20  51  28  
Underweight  12  25  9  
Total 
Figure 3.31
 Find the total for each row and column.
 Find the probability that a randomly chosen individual from this group is Tall.
 Find the probability that a randomly chosen individual from this group is Obese and Tall.
 Find the probability that a randomly chosen individual from this group is Tall, given that the individual is Obese.
 Find the probability that a randomly chosen individual from this group is Obese, given that the individual is Tall.
 Find the probability a randomly chosen individual from this group is Tall and Underweight.
 Are the events Obese and Tall independent?
5. There are several tools you can use to help organize and sort data when calculating probabilities. Contingency tables help display data and are particularly useful when calculating probabilities that have multiple dependent variables.
Use the following information to answer the next four exercises. The figure below shows a random sample of musicians and how they learned to play their instruments.
Gender  Selftaught  Studied in school  Private instruction  Total 

Female  12  38  22  72 
Male  19  24  15  58 
Total  31  62  37  130 
Figure 3.32
 Find P(musician is a female).
 Find P(musician is a male AND had private instruction).
 Find P(musician is a female OR is selftaught).
 Are the events “being a female musician” and “learning music in school” mutually exclusive events?
Solution:
b. P(musician is a male AND had private instruction) = = = 0.12
d.
 P(being a female musician AND learning music in school) = = = 0.29
 No, they are not independent because P(being a female musician AND learning music in school) is not equal to P(being a female musician)P(learning music in school).
6. An article in the New England Journal of Medicine reported about a study of smokers in California and Hawaii. In one part of the report, the selfreported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans, and 7,650 Whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 Whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 Whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 Whites.^{[1]}
Complete the table using the data provided. Suppose that one person from the study is randomly selected. Find the probability that person smoked 11 to 20 cigarettes per day.
Smoking level  African American  Native Hawaiian  Latino  Japanese Americans  White  Total 

110  
1120  
2130  
31+  
Total 
Figure 3.33
 Suppose that one person from the study is randomly selected. Find the probability that person smoked 11 to 20 cigarettes per day.
 Find the probability that the person was Latino.
 In words, explain what it means to pick one person from the study who is “Japanese American AND smokes 21 to 30 cigarettes per day.” Then find the probability.
 In words, explain what it means to pick one person from the study who is “Japanese American OR smokes 21 to 30 cigarettes per day.” Then find the probability.
 In words, explain what it means to pick one person from the study who is “Japanese American GIVEN that person smokes 21 to 30 cigarettes per day.” Then find the probability.
 Prove that smoking level and ethnicity are dependent events.
Solution:
a.
c. To pick one person from the study who is Japanese American AND smokes 21 to 30 cigarettes per day means that the person has to meet both criteria: both Japanese American and smokes 21 to 30 cigarettes. The sample space should include everyone in the study. The probability is .
e. To pick one person from the study who is Japanese American, given that person smokes 2130 cigarettes per day, means that the person must fulfill both criteria and that the sample space is reduced to those who smoke 2130 cigarettes per day. The probability is .
7. The figure below contains the number of crimes per 100,000 inhabitants from 2008 to 2011 in the US.^{[2]}
Year  Robbery  Burglary  Rape  Vehicle  Total 

2008  145.7  732.1  29.7  314.7  
2009  133.1  717.7  29.1  259.2  
2010  119.3  701  27.7  239.1  
2011  113.7  702.2  26.8  229.6  
Total 
Figure 3.34
Total each column and each row. Total data = 4,520.7.
 Find P (2009 AND Robbery).
 Find P (2010 AND Burglary).
 Find P (2010 OR Burglary).
 Find P (2011Rape).
 Find P (Vehicle2008).
Solution:
 0.0294
 0.1551
 0.7165
 0.2365
 0.2575
8. In an urn, there are 11 balls. Three balls are red (R), and eight balls are blue (B). Draw two balls, one at a time, with replacement. “With replacement” means that you put the first ball back in the urn before you select the second ball. The tree diagram using frequencies that show all the possible outcomes follows is seen in Figure 3.35 below.
Total = 64 + 24 + 24 + 9 = 121
The first set of branches represents the first draw. The second set of branches represents the second draw. Each of the outcomes is distinct. In fact, we can list each red ball as R1, R2, and R3 and each blue ball as B1, B2, B3, B4, B5, B6, B7, and B8. Then the nine RR outcomes can be written as:
R1R1R1R2R1R3R2R1R2R2R2R3R3R1R3R2R3R3
The other outcomes are similar.
There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.
 List the 24 BR outcomes: B1R1, B1R2, B1R3, …
 Using the tree diagram, calculate P(RR).
 Using the tree diagram, calculate P(RB OR BR).
 Using the tree diagram, calculate P(R on first draw AND B on second draw).
 Using the tree diagram, calculate P(R on second draw, GIVEN B on first draw).
 Using the tree diagram, calculate P(BB).
 Using the tree diagram, calculate P(B on the second draw, given R on the first draw).
Solution:
 B1R1B1R2B1R3B2R1B2R2B2R3B3R1B3R2B3R3B4R1B4R2B4R3B5R1B5R2B5R3B6R1B6R2B6R3B7R1B7R2B7R3B8R1B8R2B8R3
 P(RR) =
 P(RB OR BR) =
 P(R on first draw AND B on second draw) = P(RB) =
 P(R on second draw, GIVEN B on first draw) = P(R on second drawB on first draw) =
This problem is a conditional one. The sample space has been reduced to those outcomes that already have a blue on the first draw. There are 24 + 64 = 88 possible outcomes (24 BR and 64 BB). Twentyfour of the 88 possible outcomes are BR ().  P(BB) =
 P(B on second drawR on first draw) =
There are 9 + 24 outcomes that have R on the first draw (9 RR and 24 RB). The sample space is then 9 + 24 = 33. 24 of the 33 outcomes have B on the second draw. The probability is then .
9. An urn contains three red marbles and eight blue marbles. Draw two marbles, one at a time, from the urn, this time without replacement. “Without replacement” means that you do not put the first ball back before you select the second marble. Figure 3.36 shows a tree diagram for this situation. The branches are labeled with probabilities instead of frequencies. The numbers at the ends of the branches are calculated by multiplying the numbers on the two corresponding branches, for example:
.
Total =
NOTE: If you draw a red on the first draw from the three red possibilities, there are two red marbles left to draw on the second draw. You do not put back or replace the first marble after you have drawn it. You draw without replacement, meaning there are ten marbles left in the urn on the second draw.
Calculate the following probabilities using the tree diagram.
 P(RR)
 P(RB OR BR) = + ( )( )=
 P(R on second drawB on first draw)
 P(R on first draw AND B on second draw) = P(RB) = ( )( ) =
 P(BB)
 P(B on second drawR on first draw)
Solution:
 P(RR) =
 P(RB OR BR) =
 P(R on first draw AND B on second draw) = P(RB) =
 P(BB) =
 Using the tree diagram, P(B on second drawR on first draw) = P(RB) =
If we are using probabilities, we can label the tree in the following general way:
 P(RR) here means P(R on second drawR on first draw)
 P(BR) here means P(B on second drawR on first draw)
 P(RB) here means P(R on second drawB on first draw)
 P(BB) here means P(B on second drawB on first draw)
10. In a standard deck, there are 52 cards. 12 cards are face cards (event F), and 40 cards are not face cards (event N). Draw two cards, one at a time, with replacement. All possible outcomes are shown in the tree diagram as frequencies. Using the tree diagram, calculate P(FF).
11. In a standard deck, there are 52 cards. Twelve cards are face cards (F), and 40 cards are not face cards (N). Draw two cards, one at a time, without replacement. The tree diagram below is labeled with all possible probabilities.
 Find P(FN OR NF).
 Find P(NF).
 Find P(at most one face card).
Hint: “At most one face card” means zero or one face card.  Find P(at least one face card).
Hint: “At least one face card” means one or two face cards.
12. A litter of kittens available for adoption at the Humane Society has four tabby kittens and five black kittens. A family comes in and randomly selects two kittens (without replacement) for adoption.
 What is the probability that both kittens are tabby?
a.
b.
c.
d.
2. What is the probability that one kitten of each coloring is selected?
a.
b.
c.
d.
3. What is the probability that a tabby is chosen as the second kitten when a black kitten was chosen as the first?
4. What is the probability of choosing two kittens of the same color?
Solution:
 c
 d
13. Suppose there are four red balls and three yellow balls in a box. Two balls are drawn from the box without replacement. What is the probability that one ball of each coloring is selected?
14. Flip two fair coins. Let A = tails on the first coin and B = tails on the second coin. Then, A = {TT, TH} and B = {TT, HT}. Therefore:
 A AND B = {TT}
 A OR B = {TH, TT, HT}
The sample space when you flip two fair coins is X = {HH, HT, TH, TT}. The outcome HH is in NEITHER A NOR B. Draw a Venn diagram.
Solution:
15. Roll a fair, sixsided die. Let A = a prime number of dots being rolled. Let B = an odd number of dots being rolled. If A = {2, 3, 5} and B = {1, 3, 5}, then:
 A AND B = {3, 5}
 A OR B = {1, 2, 3, 5}
The sample space for rolling a fair die is S = {1, 2, 3, 4, 5, 6}. Draw a Venn diagram representing this situation.
16. Suppose an experiment has outcomes black, white, red, orange, yellow, green, blue, and purple, where each outcome has an equal chance of occurring. Let event C = {green, blue, purple} and event P = {red, yellow, blue}. Then C AND P = {blue} and C OR P = {green, blue, purple, red, yellow}. Draw a Venn diagram representing this situation.
17. Fifty percent of the workers at a factory work a second job, 25% have a spouse who also works, and 5% work a second job and have a spouse who also works. Draw a Venn diagram showing the relationships. Let W = working a second job and S = spouse also working.
18. A person with type O blood and a negative Rh factor (Rh) can donate blood to any person with any blood type. Four percent of African Americans have type O blood and a negative Rh factor, 5−10% of African Americans have the Rh factor, and 51% have type O blood.^{[3]} ^{[4]}
The “O” circle represents the African Americans with type O blood. The “Rh” oval represents the African Americans with the Rh factor.
We will take the average of 5% and 10%, using 7.5% as the percent of African Americans who have the Rh factor. Let O = African American with type O blood and R = African American with Rh factor.
 Find P(O).
 Find P(R).
 Find P(O AND R).
 Find P(O OR R).
 In a complete sentence, describe the overlapping area of the Venn diagram.
 In a complete sentence, describe the area of the Venn diagram in the rectangle but outside both the circle and the oval.
Solution:
 0.51
 0.075
 0.04
 0.545
 The area represents the African Americans that have type O blood and the Rh factor
 The area represents the African Americans that have neither type O blood nor the Rh factor.
19. In a bookstore, the probability that the customer buys a novel is 0.6, and the probability that the customer buys a nonfiction book is 0.4. Suppose that the probability that the customer buys both is 0.2.
 Draw a Venn diagram representing the situation.
 Find the probability that the customer buys either a novel or a nonfiction book.
 In the Venn diagram, describe the overlapping area using a complete sentence.
 Suppose that some customers buy only compact discs. Draw an oval in your Venn diagram representing this event.
20. The probability that a man develops some form of cancer in his lifetime is 0.4567. The probability that a man has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) is 0.51.^{[5]} Let: C = a man developing cancer in his lifetime and P = man having at least one false positive. Construct a tree diagram of the situation.
21. This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing three red (R), four yellow (Y), and five blue (B) beads. For the coin, P(H) = and P(T) = , where H is heads and T is tails.
Find P(tossing a head on the coin AND a red bead).
Find P(blue bead).
22. A box of cookies contains three chocolate and seven butter cookies. Miguel randomly selects a cookie and eats it. Then he randomly selects another cookie and eats it. (How many cookies did he take?)
 Draw the tree that represents the possibilities for the cookie selections. Write the probabilities along each branch of the tree.
 Are the probabilities for the flavor of the second cookie that Miguel selects independent of his first selection? Explain.
 For each complete path through the tree, write the event it represents and find the probabilities.
 Let S be the event that both cookies selected were the same flavor. Find P(S).
 Let T be the event that the cookies selected were different flavors. Find P(T) by two different methods, using the complement rule and using the branches of the tree. Your answers should be the same with both methods.
 Let U be the event that the second cookie selected is a butter cookie. Find P(U).
23. Suppose that you have eight cards. Five are green, and three are yellow. The cards are well shuffled.
Suppose that you randomly draw two cards, one at a time, with replacement. Let G_{1} = first card is green and G_{2} = second card is green.
 Draw a tree diagram of the situation.
 Find P(G_{1} AND G_{2}).
 Find P(at least one green).
 Find P(G_{2}G_{1}).
 Are G_{2} and G_{1} independent events? Explain why or why not.
Solution:
 P(GG) = =
 P(at least one green) = P(GG) + P(GY) + P(YG) = + + =
 P(GG) =
 Yes, they are independent because the first card is placed back in the bag before the second card is drawn; the composition of cards in the bag remains the same from Draw 1 to Draw 2.
Suppose that you randomly draw two cards, one at a time, without replacement. Let G_{1} = first card is green and G_{2} = second card is green.
 Draw a tree diagram of the situation.
 Find P(G_{1} AND G_{2}).
 Find P(at least one green).
 Find P(G_{2}G_{1}).
 Are G_{2} and G_{1} independent events? Explain why or why not.
24. The percent of licensed US drivers (from a recent year) that are female is 48.60. Of the females, 5.03% are age 19 and under; 81.36% are age 20–64; and 13.61% are age 65 or over. Of the licensed US male drivers, 5.04% are age 19 and under; 81.43% are age 20–64; and 13.53% are age 65 or over.^{[6]}
Complete the following:
 Construct a table or a tree diagram of the situation.
 Find P(driver is female).
 Find P(driver is age 65 or overdriver is female).
 Find P(driver is age 65 or over AND female).
 In words, explain the difference between the probabilities in part (c) and part (d).
 Find P(driver is age 65 or over).
 Are being age 65 or over and being female mutually exclusive events? How do you know?
Solution:

<20 2064 >64 Total Female 0.0244 0.3954 0.0661 0.486 Male 0.0259 0.4186 0.0695 0.514 Total 0.0503 0.8140 0.1356 1 Figure 3.46
 P(F) = 0.486
 P(>64F) = 0.1361
 P(>64 and F) = P(F) P(>64F) = (0.486)(0.1361) = 0.0661
 P(>64F) is the percentage of female drivers who are 65 or older, and P(>64 and F) is the percentage of drivers who are female and 65 or older.
 P(>64) = P(>64 and F) + P(>64 and M) = 0.1356
 No, being female and 65 or older are not mutually exclusive because they can occur at the same time P(>64 and F) = 0.0661.
Suppose that 10,000 US licensed drivers are randomly selected.
 How many would you expect to be male?
 Using the table or tree diagram, construct a contingency table of gender versus age group.
 Using the contingency table, find the probability that a driver randomly selected from the 20–64 age group is female.
25. Approximately 86.5% of Americans commute to work by car, truck, or van. Out of that group, 84.6% drive alone and 15.4% drive in a carpool. Approximately 3.9% walk to work, and approximately 5.3% take public transportation.^{[7]}
 Construct a table or a tree diagram of the situation. Include a branch for all other modes of transportation to work.
 Assuming that the walkers walk alone, what percent of all commuters travel alone to work?
 Suppose that 1,000 workers are randomly selected. How many would you expect to travel alone to work?
 Suppose that 1,000 workers are randomly selected. How many would you expect to drive in a carpool?
Solution:

Car, truck, or van Walk Public transportation Other Totals Alone 0.7318 Not alone 0.1332 Totals 0.8650 0.0390 0.0530 0.0430 1 Figure 3.47
 If we assume that all walkers are alone and that no one from the other two groups travel alone (which is a big assumption), we have: P(Alone) = 0.7318 + 0.0390 = 0.7708.
 Making the same assumptions as in (b), we have: (0.7708)(1,000) = 771
 (0.1332)(1,000) = 133
26. When the Euro coin was introduced in 2002, two math professors had their statistics students test whether the Belgian one Euro coin was a fair coin. They spun the coin rather than tossing it and found that 140 of 250 spins showed a head (event H), while 110 showed a tail (event T). On that basis, they claimed that it is not a fair coin.
 Based on the given data, find P(H) and P(T).
 Use a tree to find the probabilities of each possible outcome for the experiment of tossing the coin twice.
 Use the tree to find the probability of obtaining exactly one head in two tosses of the coin.
 Use the tree to find the probability of obtaining at least one head.
27. The following are real data from Santa Clara County, CA. At a certain point in time, there had been a total of 3,059 documented cases of AIDS in the county. They were grouped into the following categories:^{[8]}
Homosexual/bisexual  IV drug user*  Heterosexual contact  Other  Total  

Female  0  70  136  49  
Male  2,146  463  60  135  
Total  
*includes homosexual/bisexual IV drug users 
Figure 3.48
Suppose a person with AIDS in Santa Clara County is randomly selected.
 Find P(person is female).
 Find P(person has a risk factor heterosexual contact).
 Find P(person is female OR has a risk factor of IV drug user).
 Find P(person is female AND has a risk factor of homosexual/bisexual).
 Find P(person is male AND has a risk factor of IV drug user).
 Find P(person is female, GIVEN person got the disease from heterosexual contact).
 Construct a Venn diagram. Make one group females and the other group heterosexual contact.
The completed contingency table is as follows:
Homosexual/bisexual  IV drug user*  Heterosexual contact  Other  Total  

Female  0  70  136  49  255 
Male  2,146  463  60  135  2,804 
Total  2,146  533  196  184  3,059 
*includes homosexual/bisexual IV drug users 
Figure 3.49
Solution:
 0
Answer these questions using probability rules. Do NOT use the contingency table. Three thousand fiftynine cases of AIDS had been reported in Santa Clara County, CA, through a certain date. Those cases will be our population. Of those cases, 6.4% obtained the disease through heterosexual contact and 7.4% are female. Out of the females with the disease, 53.3% got the disease from heterosexual contact.
 Find P(person is female).
 Find P(person obtained the disease through heterosexual contact).
 Find P(person is female, GIVEN person got the disease from heterosexual contact).
 Construct a Venn diagram representing this situation. Make one group females and the other group heterosexual contact. Fill in all values as probabilities.
28. The table shows the political party affiliation of each of 67 members of the US Senate in June 2012 and when they are up for reelection.^{[9]}
Up for reelection  Democratic party  Republican party  Other  Total 

November 2014  20  13  0  
November 2016  10  24  0  
Total 
Figure 3.51
 What is the probability that a randomly selected senator has an “Other” affiliation?
 What is the probability that a randomly selected senator is up for reelection in November 2016?
 What is the probability that a randomly selected senator is a Democrat and up for reelection in November 2016?
 What is the probability that a randomly selected senator is a Republican or is up for reelection in November 2014?
 Suppose that a member of the US Senate is randomly selected. Given that the randomly selected senator is up for reelection in November 2016, what is the probability that this senator is a Democrat?
 Suppose that a member of the US Senate is randomly selected. What is the probability that the senator is up for reelection in November 2014, knowing that this senator is a Republican?
 The events “Republican” and “Up for reelection in 2016” are .
 mutually exclusive
 independent
 both mutually exclusive and independent
 neither mutually exclusive nor independent
 The events “Other” and “Up for reelection in November 2016” are .
 mutually exclusive
 independent
 both mutually exclusive and independent
 neither mutually exclusive nor independent
Solution:
a. 0
c.
e.
29. The figure below gives the number of suicides estimated in the US for a recent year by age, race (Black or White), and sex. We are interested in possible relationships between age, race, and sex. We will let suicide victims be our population.
Race and sex  114  1524  2564  Over 64  Total 

White, male  210  3,360  13,610  22,050  
White, female  80  580  3,380  4,930  
Black, male  10  460  1,060  1,670  
Black, female  0  40  270  330  
All others  
Total  310  4,650  18,780  29,760 
Figure 3.52
Do not include “all others.”
 Fill in the column for the suicides for individuals over age 64.
 Fill in the row for all other races.
 Find the probability that a randomly selected individual was a White male.
 Find the probability that a randomly selected individual was a Black female.
 Find the probability that a randomly selected individual was Black.
 Find the probability that a randomly selected individual was a Black or White male. Do not include “all others.”
 Out of the individuals over age 64, find the probability that a randomly selected individual was a Black or White male. Do not include “all others.”
Solution:

Race and sex 114 1524 2564 Over 64 Total White, male 210 3,360 13,610 4,870 22,050 White, female 80 580 3,380 890 4,930 Black, male 10 460 1,060 140 1,670 Black, female 0 40 270 20 330 All others 100 Total 310 4,650 18,780 6,020 29,760 Figure 3.53

Race and sex 114 1524 2564 Over 64 Total White, male 210 3,360 13,610 4,870 22,050 White, female 80 580 3,380 890 4,930 Black, male 10 460 1,060 140 1,670 Black, female 0 40 270 20 330 All others 10 210 460 100 780 Total 310 4,650 18,780 6,020 29,760 Figure 3.54
30. The table of data obtained from the website Baseball Almanac shows hit information for four wellknown baseball players. Suppose that one hit from the table is randomly selected.^{[10]}
Name  Single  Double  Triple  Home run  Total hits 

Babe Ruth  1,517  506  136  714  2,873 
Jackie Robinson  1,054  273  54  137  1,518 
Ty Cobb  3,603  174  295  114  4,189 
Hank Aaron  2,294  624  98  755  3,771 
Total  8,471  1,577  583  1,720  12,351 
Figure 3.55
Find P(hit was made by Babe Ruth).
Find P(hit was made by Ty Cobbhit was a home run).
31. The figure below identifies a group of children by one of four hair colors and by type of hair.
Hair type  Brown  Blond  Black  Red  Total 

Wavy  20  15  3  43  
Straight  80  15  12  
Total  20  215 
Figure 3.56
 Complete the table.
 What is the probability that a randomly selected child will have wavy hair?
 What is the probability that a randomly selected child will have either brown or blond hair?
 What is the probability that a randomly selected child will have wavy brown hair?
 What is the probability that a randomly selected child will have red hair, given that he or she has straight hair?
 If B is the event of a child having brown hair, find the probability of the complement of B.
 In words, what does the complement of B represent?
32. In a previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury News. The factual data were compiled into the following table.^{[11]}
Shirt number  ≤ 210  211–250  251–290  > 290 

133  21  5  0  0 
3466  6  18  7  4 
6699  6  12  22  5 
Figure 3.57
For the following, suppose that you randomly select one player from the 49ers or Cowboys.
 Find the probability that his shirt number is from 1 to 33.
 Find the probability that he weighs at most 210 pounds.
 Find the probability that his shirt number is from 1 to 33 AND he weighs at most 210 pounds.
 Find the probability that his shirt number is from 1 to 33 OR he weighs at most 210 pounds.
 Find the probability that his shirt number is from 1 to 33, GIVEN that he weighs at most 210 pounds.
Solution:
3.2 Visualizing Bivariate Quantitative Data
1. The Gross Domestic Product Purchasing Power Parity (GDP PPP) is an indication of a country’s currency value compared to another country. The figure below shows the GDP PPP of Cuba as compared to US dollars. Construct a scatter plot of the data.
Year  Cuba's PPP  Year  Cuba's PPP 

1999  1,700  2006  4,000 
2000  1,700  2007  11,000 
2002  2,300  2008  9,500 
2003  2,900  2009  9,700 
2004  3,000  2010  9,900 
2005  3,500 
Figure 3.58
2. The following table shows the poverty rates and cell phone usage in the United States. Construct a scatter plot of the data.
Year  Poverty rate  Cellular usage per capita 

2003  12.7  54.67 
2005  12.6  74.19 
2007  12  84.86 
2009  12  90.82 
Figure 3.59
3. Does higher cost of tuition translate into higherpaying jobs? The table lists the top ten colleges based on midcareer salary and the associated yearly tuition costs. Construct a scatter plot of the data. Note that tuition is the independent variable and salary is the dependent variable.
School  Midcareer salary (in thousands)  Yearly tuition 

Princeton  137  28,540 
Harvey Mudd  135  40,133 
CalTech  127  39,900 
US Naval Academy  122  0 
West Point  120  0 
MIT  118  42,050 
Lehigh University  118  43,220 
NYUPoly  117  39,565 
Babson College  117  40,400 
Stanford  114  54,506 
Figure 3.60
3.3 Measures of Association
1. Can a coefficient of determination be negative? Why or why not?
2. The Gross Domestic Product Purchasing Power Parity is an indication of a country’s currency value compared to another country. The figure below shows the GDP PPP of Cuba as compared to US dollars. Construct a scatter plot of the data.
Year  Cuba's PPP  Year  Cuba's PPP 

1999  1,700  2006  4,000 
2000  1,700  2007  11,000 
2002  2,300  2008  9,500 
2003  2,900  2009  9,700 
2004  3,000  2010  9,900 
2005  3,500 
Figure 3.61
Find:
 r
 r^{2x}
3. The following table shows the poverty rates and cell phone usage in the United States. Construct a scatter plot of the data.
Year  Poverty rate  Cellular usage per capita 

2003  12.7  54.67 
2005  12.6  74.19 
2007  12  84.86 
2009  12  90.82 
Figure 3.62
Find:
 r
 r^{2}
4. Does the higher cost of tuition translate into higherpaying jobs? The table lists the top ten colleges based on midcareer salary and the associated yearly tuition costs. Construct a scatter plot of the data. Note that tuition is the independent variable and salary is the dependent variable.
School  Midcareer salary (in thousands)  Yearly tuition 

Princeton  137  28,540 
Harvey Mudd  135  40,133 
CalTech  127  39,900 
US Naval Academy  122  0 
West Point  120  0 
MIT  118  42,050 
Lehigh University  118  43,220 
NYUPoly  117  39,565 
Babson College  117  40,400 
Stanford  114  54,506 
Figure 3.63
Find:
 r
 r^{2}
3.4 Modeling Linear Relationships
1. A random sample of ten professional athletes produced the following data, where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars).
0  2  5  12 
3  8  4  9 
2  7  3  9 
1  3  0  3 
5  13  4  10 
Figure 3.64
 Draw a scatter plot of the data.
 Use regression to find the equation for the line of best fit.
 Draw the line of best fit on the scatter plot.
 What is the slope of the line of best fit? What does it represent?
 What is the yintercept of the line of best fit? What does it represent?
 What does an r value of zero mean?
 When n = 2 and r = 1, are the data significant? Explain.
 When n = 100 and r = 0.89, is there a significant correlation? Explain.
Solution:
b. ŷ = 2.23 + 1.99x
d. The slope is 1.99 (b = 1.99). It means that, for every endorsement deal a professional player gets, he gets an average of another $1.99 million in pay each year.
f. It means that there is no correlation between the datasets.
h. Yes, there are enough data points, and the value of r is strong enough to show that there is a strong negative correlation between the datasets.
2. What is the process through which we can calculate a line that goes through a scatter plot with a linear pattern?
3.5 Cautions about Regression
1. The following table shows economic development measured in per capita income (PCINC).
Year  PCINC  year  PCINC 

1870  340  1920  1050 
1880  499  1930  1170 
1890  592  1940  1364 
1900  757  1950  1836 
1910  927  1960  2132 
Figure 3.65
 What are the independent and dependent variables?
 Draw a scatter plot.
 Use regression to find the line of best fit and the correlation coefficient.
 Interpret the significance of the correlation coefficient.
 Is there a linear relationship between the variables?
 Find the coefficient of determination and interpret it.
 What is the slope of the regression equation? What does it mean?
 Use the line of best fit to estimate PCINC for 1900 and for 2000.
 Determine if there are any outliers.
2. The scatter plot shows the relationship between hours spent studying and exam scores. The line shown is the calculated line of best fit. The correlation coefficient is 0.69.
 Do there appear to be any outliers?
 A point is removed, and the line of best fit is recalculated. The new correlation coefficient is 0.98. Does the point appear to have been an outlier? Why?
 What effect did the potential outlier have on the line of best fit?
 Are you more or less confident in the predictive ability of the new line of best fit?
 The sum of squared errors for a dataset of 18 numbers is 49. What is the standard deviation?
 The standard deviation for the sum of squared errors for a dataset is 9.8. What is the cutoff for the vertical distance that a point can be from the line of best fit to be considered an outlier?
Solution:
a. Yes, there appears to be an outlier at (6, 58).
c. The potential outlier flattened the slope of the line of best fit because it was below the dataset. It made the line of best fit less accurate as a predictor for the data.
e. s = 1.75
3. The heights (sidewalk to roof) of notable tall buildings in America are compared to the number of stories of the building (beginning at street level).
Height (in feet)  Stories 

1,050  57 
428  28 
362  26 
529  40 
790  60 
401  22 
380  38 
1,454  110 
1,127  100 
700  46 
Figure 3.67
 Using “stories” as the independent variable and “height” as the dependent variable, make a scatter plot of the data.
 Does it appear from inspection that there is a relationship between the variables?
 Calculate the leastsquares line. Put the equation in the form of: ŷ = a + bx.
 Find the correlation coefficient. Is it significant?
 Find the estimated heights for 32 stories and for 94 stories.
 Based on the data, is there a linear relationship between the number of stories in tall buildings and the height of the buildings?
 Are there any outliers in the data? If so, which point(s)?
 What is the estimated height of a building with six stories? Does the leastsquares line give an accurate estimate of height? Explain why or why not.
 Based on the leastsquares line, adding an extra story is predicted to add about how many feet to a building?
 What is the slope of the leastsquares (bestfit) line? Interpret the slope.
4. Ornithologists, scientists who study birds, tag sparrow hawks in 13 different colonies to study their population. They gather data for the percent of new sparrow hawks in each colony and the percent of those that have returned from migration.
Percent returning: 74, 66, 81, 52, 73, 62, 52, 45, 62, 46, 60, 46, 38
Percent new: 5, 6, 8, 11, 12, 15, 16, 17, 18, 18, 19, 20, 20
 Enter the data into your calculator and make a scatter plot.
 Use your calculator’s regression function to find the equation of the leastsquares regression line. Add this to your scatter plot from (a).
 Explain in words what the slope and yintercept of the regression line tell us.
 How well does the regression line fit the data? Explain your response.
 Which point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain.
 An ecologist wants to predict how many birds will join another colony of sparrow hawks to which 70% of the adults from the previous year have returned. What is the prediction?
Solution:
 Check student’s solution.
 Check student’s solution.
 The slope of the regression line is 0.3031 with a yintercept of 31.93. In context, the yintercept indicates that, when there are no returning sparrow hawks, there will be almost 32% new sparrow hawks, which doesn’t make sense since, if there are no returning birds, then the new percentage would have to be 100% (this is an example of why we do not extrapolate). The slope tells us that for each percentage increase in returning birds, the percentage of new birds in the colony decreases by 30.3%.
 If we examine r^{2}, we see that only 57.52% of the variation in the percent of new birds is explained by the model, and the correlation coefficient, r = –0.7584, only indicates a somewhat strong correlation between returning and new percentages.
 The ordered pair (66, 6) generates the largest residual of 6.0. This means that, when the observed return percentage is 66%, our observed new percentage, 6%, is almost 6% less than the predicted new value of 11.98%. If we remove this data pair, we see only an adjusted slope of 0.2789 and an adjusted intercept of 30.9816. In other words, even though this data generates the largest residual, it is not an outlier, nor is the data pair an influential point.
 If there are 70% returning birds, we would expect to see y = –0.2789(70) + 30.9816 = 0.114 or 11.4% new birds in the colony.
5. The following table shows data on average per capita coffee consumption and heart disease rate in a random sample of ten countries.
Coffee consumption and heart disease  

Yearly coffee consumption in liters  2.5  3.9  2.9  2.4  2.9  0.8  9.1  2.7  0.8  0.7 
Death from heart diseases  221  167  131  191  220  297  71  172  211  300 
Figure 3.68
 Enter the data into your calculator, and make a scatter plot.
 Use your calculator’s regression function to find the equation of the leastsquares regression line. Add this to your scatter plot from (a).
 Explain in words what the slope and yintercept of the regression line tell us.
 How well does the regression line fit the data? Explain your response.
 Which point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain.
 Do the data provide convincing evidence that there is a linear relationship between the amount of coffee consumed and the heart disease death rate? Carry out an appropriate test at a significance level of 0.05 to help answer this question.
6. The following table consists of one student athlete’s time (in minutes) to swim 2,000 yards and the student’s heart rate (beats per minute) after swimming on a random sample of ten days:
Swim time  Heart rate 

34.12  144 
35.72  152 
34.72  124 
34.05  140 
34.13  152 
35.73  146 
36.17  128 
35.57  136 
35.37  144 
35.57  148 
Figure 3.69
 Enter the data into your calculator and make a scatter plot.
 Use your calculator’s regression function to find the equation of the leastsquares regression line. Add this to your scatter plot from (a).
 Explain in words what the slope and yintercept of the regression line tell us.
 How well does the regression line fit the data? Explain your response.
 Which point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain.
Solution:
 Check student’s solution.
 Check student’s solution.
 We have a slope of –1.4946 with a yintercept of 193.88. In context, the slope indicates that, for each additional minute added to the swim time, the heart rate will decrease by 1.5 beats per minute. If the student is not swimming at all, the yintercept indicates that his heart rate will be 193.88 beats per minute. While the slope has meaning (i.e., the longer it takes to swim 2,000 meters, the less effort the heart puts out), the yintercept does not make sense. If the athlete is not swimming (resting), then his heart rate should be very low.
 Since only 1.5% of the heart rate variation is explained by this regression equation, we must conclude that this association is not explained with a linear relationship.
 The point (34.72, 124) generates the largest residual of –11.82. This means that our observed heart rate is almost 12 beats less than our predicted rate of 136 beats per minute. When this point is removed, the slope becomes –2.953 with the yintercept changing to 247.1616. While the linear association is still very weak, we see that the removed data pair can be considered an influential point in the sense that the yintercept becomes more meaningful.
7. A researcher is investigating whether population impacts homicide rate. He uses demographic data from Detroit, MI, to compare homicide rates and the number of the population that are White males.
Population size  Homicide rate per 100,000 people 

558,724  8.6 
538,584  8.9 
519,171  8.52 
500,457  8.89 
482,418  13.07 
465,029  14.57 
448,267  21.36 
432,109  28.03 
416,533  31.49 
401,518  37.39 
387,046  46.26 
373,095  47.24 
359,647  52.33 
Figure 3.70
 Use your calculator to construct a scatter plot of the data. What should the independent variable be? Why?
 Use your calculator’s regression function to find the equation of the leastsquares regression line. Add this to your scatter plot.
 Discuss what the following mean in context:
 The slope of the regression equation
 The yintercept of the regression equation
 The correlation r
 The coefficient of determination r^{2}
 Do the data provide convincing evidence that there is a linear relationship between population size and homicide rate? Carry out an appropriate test at a significance level of 0.05 to help answer this question.
8. Use the table below to answer (a) and (b).
School  Midcareer salary (in thousands)  Yearly tuition 

Princeton  137  28,540 
Harvey Mudd  135  40,133 
CalTech  127  39,900 
US Naval Academy  122  0 
West Point  120  0 
MIT  118  42,050 
Lehigh University  118  43,220 
NYUPoly  117  39,565 
Babson College  117  40,400 
Stanford  114  54,506 
Figure 3.71
 Use the data to determine the linearregression line equation with the outliers removed. Is there a linear correlation for the dataset with outliers removed? Justify your answer.
 If we remove the two service academies (the tuition is $0.00), we construct a new regression equation of y = –0.0009x + 160 with a correlation coefficient of 0.71397 and a coefficient of determination of 0.50976. This allows us to say there is a fairly strong linear association between tuition costs and salaries if the service academies are removed from the dataset.
9. The average number of people in a family that attended college for various years is given below.
Year  Number of family members attending college 

1969  4.0 
1973  3.6 
1975  3.2 
1979  3.0 
1983  3.0 
1988  3.0 
1991  2.9 
Figure 3.72
 Using “Year” as the independent variable and “Number of Family Members Attending College” as the dependent variable, draw a scatter plot of the data.
 Calculate the leastsquares line. Put the equation in the form of: ŷ = a + bx.
 Find the correlation coefficient. Is it significant?
 Pick two years between 1969 and 1991, and find the estimated number of family members attending college.
 Based on the data, is there a linear relationship between the year and the average number of family members attending college?
 Using the leastsquares line, estimate the number of family members attending college for 1960 and 1995. Does the leastsquares line give an accurate estimate for those years? Explain why or why not.
 Are there any outliers in the data?
 What is the estimated average number of family members attending college for 1986? Does the leastsquares line give an accurate estimate for that year? Explain why or why not.
 What is the slope of the leastsquares (bestfit) line? Interpret the slope.
10. The percent of female wage and salary workers who are paid hourly rates is given in below for the years 1979 to 1992.
Year  Percent of workers paid hourly rates 

1979  61.2 
1980  60.7 
1981  61.3 
1982  61.3 
1983  61.8 
1984  61.7 
1985  61.8 
1986  62.0 
1987  62.7 
1990  62.8 
1992  62.9 
Figure 3.73
 Using the year as the independent variable and the percent as the dependent variable, draw a scatter plot of the data.
 Does it appear from inspection that there is a relationship between the variables? Why or why not?
 Calculate the leastsquares line. Put the equation in the form of: ŷ = a + bx.
 Find the correlation coefficient. Is it significant?
 Find the estimated percents for 1988 and 1991.
 Based on the data, is there a linear relationship between the year and the percent of female wage and salary earners who are paid hourly rates?
 Are there any outliers in the data?
 What is the estimated percent for the year 2050? Does the leastsquares line give an accurate estimate for that year? Explain why or why not.
 What is the slope of the leastsquares (bestfit) line? Interpret the slope.
Solution:
 Check student’s solution.
 Yes
 ŷ = −266.8863+0.1656x
 0.9448; yes
 62.8233; 62.3265
 Yes
 No; (1987, 62.7)
 72.5937; no
 Slope = 0.1656.
As the year increases by one, the percent of workers paid hourly rates tends to increase by 0.1656.
11. The cost of a leading liquid laundry detergent in different sizes is given below.
Size (ounces)  Cost ($)  Cost per ounce 

16  3.99  
32  4.99  
64  5.00  
200  10.99 
Figure 3.74
 Complete the table for the cost per ounce of the different sizes.
 Using size as the independent variable and cost per ounce as the dependent variable, draw a scatter plot of the data.
 Does it appear from inspection that there is a relationship between the variables? Why or why not?
 Calculate the leastsquares line. Put the equation in the form of: ŷ = a + bx.
 Find the correlation coefficient. Is it significant?
 If the laundry detergent were sold in a 40ounce size, find the estimated cost per ounce.
 If the laundry detergent were sold in a 90ounce size, find the estimated cost per ounce.
 Does it appear that a line is the best way to fit the data? Why or why not?
 Are there any outliers in the data?
 Is the leastsquares line valid for predicting what a 300ounce size of the laundry detergent would cost per ounce? Why or why not?
 What is the slope of the leastsquares (bestfit) line? Interpret the slope.
Solution:

Size (ounces) Cost ($) Cost/oz 16 3.99 24.94 32 4.99 15.59 64 5.00 9.36 200 10.99 5.50 Figure 3.75
 Check student’s solution.
 There is a linear relationship for the sizes 16 through 64, but that linear trend does not continue to the 200oz size.
 ŷ = 20.2368 – 0.0819x
 r = –0.8086
 40oz: 16.96 cents/oz
 90oz: 12.87 cents/oz
 The relationship is not linear; the leastsquares line is not appropriate.
 No outliers
 No, you would be extrapolating. The 300oz size is outside the range of x.
 Slope = –0.08194; for each additional ounce in size, the cost per ounce decreases by 0.082 cents.
12. According to a flyer by a Prudential Insurance Company representative, the costs of approximate probate fees and taxes for selected net taxable estates are as follows:
Net taxable estate ($)  Approximate probate fees and taxes ($) 

600,000  30,000 
750,000  92,500 
1,000,000  203,000 
1,500,000  438,000 
2,000,000  688,000 
2,500,000  1,037,000 
3,000,000  1,350,000 
Figure 3.76
 Decide which variable should be the independent variable and which should be the dependent variable.
 Draw a scatter plot of the data.
 Does it appear from inspection that there is a relationship between the variables? Why or why not?
 Calculate the leastsquares line. Put the equation in the form of: ŷ = a + bx.
 Find the correlation coefficient. Is it significant?
 Find the estimated total cost for a next taxable estate of $1,000,000. Find the cost for $2,500,000.
 Does it appear that a line is the best way to fit the data? Why or why not?
 Are there any outliers in the data?
 Based on these results, what would be the probate fees and taxes for an estate that does not have any assets?
 What is the slope of the leastsquares (bestfit) line? Interpret the slope.
13. The following are advertised sale prices of color televisions at Anderson’s.
Size (inches)  Sale price ($) 

9  147 
20  197 
27  297 
31  447 
35  1,277 
40  2,177 
60  2,497 
Figure 3.77
 Decide which variable should be the independent variable and which should be the dependent variable.
 Draw a scatter plot of the data.
 Does it appear from inspection that there is a relationship between the variables? Why or why not?
 Calculate the leastsquares line. Put the equation in the form of: ŷ = a + bx.
 Find the correlation coefficient. Is it significant?
 Find the estimated sale price for a 32inch television. Find the cost for a 50inch television.
 Does it appear that a line is the best way to fit the data? Why or why not?
 Are there any outliers in the data?
 What is the slope of the leastsquares (bestfit) line? Interpret the slope.
Solution:
 The independent variable is size (x), and the dependent variable is price (y).
 Check student’s solution.
 The relationship does not appear to be linear.
 ŷ = –745.252 + 54.75569x
 r = 0.8944; yes it is significant
 32inch: $1,006.93, 50inch: $1,992.53
 No, the relationship does not appear to be linear. However, r is significant.
 No, the 60inch TV
 For each additional inch, the price increases by $54.76.
14. The figure below shows the average heights for American boys in 1990.
Age (years)  Height (cm) 

birth  50.8 
2  83.8 
3  91.4 
5  106.6 
7  119.3 
10  137.1 
14  157.5 
Figure 3.78
 Decide which variable should be the independent variable and which should be the dependent variable.
 Draw a scatter plot of the data.
 Does it appear from inspection that there is a relationship between the variables? Why or why not?
 Calculate the leastsquares line. Put the equation in the form of: ŷ = a + bx.
 Find the correlation coefficient. Is it significant?
 Find the estimated average height for a oneyearold. Find the estimated average height for an 11yearold.
 Does it appear that a line is the best way to fit the data? Why or why not?
 Are there any outliers in the data?
 Use the leastsquares line to estimate the average height for a 62yearold man. Do you think that your answer is reasonable? Why or why not?
 What is the slope of the leastsquares (bestfit) line? Interpret the slope.
15. Use the table below to answer (a)–(n).
State  Number of letters in name  Year entered the Union  Ranks for entering the Union  Area (square miles) 

Alabama  7  1819  22  52,423 
Colorado  8  1876  38  104,100 
Hawaii  6  1959  50  10,932 
Iowa  4  1846  29  56,276 
Maryland  8  1788  7  12,407 
Missouri  8  1821  24  69,709 
New Jersey  9  1787  3  8,722 
Ohio  4  1803  17  44,828 
South Carolina  13  1788  8  32,008 
Utah  4  1896  45  84,904 
Wisconsin  9  1848  30  65,499 
Figure 3.79
We are interested in whether there is a relationship between the ranking of a state and the area of the state.
 What are the independent and dependent variables?
 What do you think the scatter plot will look like? Make a scatter plot of the data.
 Does it appear from inspection that there is a relationship between the variables? Why or why not?
 Calculate the leastsquares line. Put the equation in the form of: ŷ = a + bx.
 Find the correlation coefficient. What does it imply about the significance of the relationship?
 Find the estimated areas for Alabama and for Colorado. Are they close to the actual areas?
 Use the two points in (f) to plot the leastsquares line on your graph from (b).
 Does it appear that a line is the best way to fit the data? Why or why not?
 Are there any outliers?
 Use the leastsquares line to estimate the area of a new state that enters the Union. Can the leastsquares line be used to predict it? Why or why not?
 Delete “Hawaii” and substitute “Alaska” for it. Alaska is the 49th state, with an area of 656,424 square miles. Calculate the new leastsquares line.
 Find the estimated area for Alabama. Is it closer to the actual area with this new leastsquares line or with the previous one that included Hawaii? Why do you think that’s the case?
 Do you think that, in general, newer states are larger than the original states?
Solution:
 Let rank be the independent variable and area be the dependent variable.
 Check student’s solution.
 There appears to be a linear relationship, with one outlier.
 ŷ (area) = 24,177.06 + 1,010.478x
 r = 0.50047; r is not significant, so there is no relationship between the variables.
 Alabama: 46,407.576; Colorado: 62,575.224
 Alabama estimate is closer than Colorado estimate.
 If the outlier is removed, there is a linear relationship.
 There is one outlier (Hawaii).
 Rank 51: 75,711.4; no
 ŷ = –87065.3 + 7828.532x
 Alabama: 85,162.404; the prior estimate was closer. Alaska is an outlier.
 Yes, with the exception of Hawaii
References
Figures
Figure 3.35: Figure 3.10 from OpenStax Statistics (2020) (CC BY 4.0). Retrieved from https://openstax.org/books/statistics/pages/35treeandvenndiagrams
Figure 3.36: Figure 3.13 from OpenStax Statistics (2020) (CC BY 4.0). Retrieved from https://openstax.org/books/statistics/pages/35treeandvenndiagrams
Figure 3.37: Figure from OpenStax Statistics (2020) (CC BY 4.0). Retrieved from https://openstax.org/books/statistics/pages/35treeandvenndiagrams
Figure 3.38: Figure 3.12 from OpenStax Statistics (2020) (CC BY 4.0). Retrieved from https://openstax.org/books/statistics/pages/35treeandvenndiagrams
Figure 3.39: Figure 3.14 from OpenStax Statistics (2020) (CC BY 4.0). Retrieved from https://openstax.org/books/statistics/pages/35treeandvenndiagrams
Figure 3.40: Figure from OpenStax Statistics (2020) (CC BY 4.0). Retrieved from https://openstax.org/books/statistics/pages/35treeandvenndiagrams
Figure 3.41: Figure 3.16 from OpenStax Statistics (2020) (CC BY 4.0). Retrieved from https://openstax.org/books/statistics/pages/35treeandvenndiagrams
Figure 3.42: Figure 3.18 from OpenStax Statistics (2020) (CC BY 4.0). Retrieved from https://openstax.org/books/statistics/pages/35treeandvenndiagrams
Figure 3.43: Figure 3.15 from OpenStax Introductory Statistics (2013) (CC BY 4.0). Retrieved from https://openstax.org/books/introductorystatistics/pages/3solutions#element750solution
Text
Data from the House Ways and Means Committee, the Health and Human Services Department.
Data from Microsoft Bookshelf.
Data from the United States Department of Labor, the Bureau of Labor Statistics.
Data from the Physician’s Handbook, 1990.
 Haiman, Christopher A., Daniel O. Stram, Lynn R. Wilkens, Malcom C. Pike, Laurence N. Kolonel, Brien E. Henderson, and Loīc Le Marchand. “Ethnic and Racial Differences in the SmokingRelated Risk of Lung Cancer.” The New England Journal of Medicine, 2013. Available online at http://www.nejm.org/doi/full/10.1056/NEJMoa033250 (accessed May 2, 2013). ↵
 "United States: Uniform Crime Report – State Statistics from 1960–2011.” The Disaster Center. Available online at http://www.disastercenter.com/crime (accessed May 2, 2013). ↵
 “Blood Types.” American Red Cross, 2013. Available online at http://www.redcrossblood.org/learnaboutblood/bloodtypes (accessed May 3, 2013). ↵
 Samuel, T. M. “Strange Facts about RH Negative Blood.” Healthfully, 2017. Available online at https://healthfully.com/strangerhnegativeblood5552003.html (accessed January 26, 2021). ↵
 Data from the American Cancer Society. ↵
 Data from the Federal Highway Administration, part of the United States Department of Transportation. ↵
 Data from the Federal Highway Administration, part of the United States Department of Transportation. ↵
 Data from Santa Clara County Public Health Department ↵
 Data from United States Senate. Available online at www.senate.gov (accessed May 2, 2013). ↵
 Data from the BaseballAlmanac, 2013. Available online at www.baseballalmanac.com (accessed May 2, 2013). ↵
 Data from the San Jose Mercury News. ↵