Witte & Witte, 10e Page of Pages



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Witte & Witte, 10e Page of Pages

Chapter 8



Chapter 8: Populations, Samples, and Probability
Exercise 1
For each of the following pairs, indicate with a Yes or No whether the relationship between the first and second expressions could describe that between a sample and its population, respectively.


  1. Third graders in Minneapolis; third graders in Minnesota

  2. Registered voters in Wisconsin; retirees residing in Wisconsin

  3. Members of the University of Kentucky men’s basketball team; student athletes at the University of Kentucky

  4. History majors at Marquette University; history majors in the United States

  5. Psychology majors in Connecticut; psychology majors at Yale University

  6. Books written by Edgar Allan Poe; books written by American authors

  7. Married women residing in Austin, Texas; married women residing in Texas.

  8. Brad Pitt; Australian actors

Answers:


  1. Yes

  2. No

  3. Yes

  4. Yes

  5. No

  6. Yes

  7. Yes

  8. No


Exercise 2
Which of the following would be considered hypothetical populations?


  1. Persons who received a flu shot at a local hospital last October

  2. Married couples who will still be married to each other in five years.

  3. Persons who received a speeding ticket in Illinois last year

  4. Freshmen students who will graduate from Ohio University within four years

  5. Women who will suffer from severe depression sometime during their lives.

Answer:


b, d, and e are hypothetical populations
Exercise 3
Dr. Sue Rogers needs four participants for a psychological experiment. She plans to randomly select four persons from the group shown below. Indicate whether each of the following statements is True or False.


Tom

George

Joe

Hank

Mary

Ellen

Jane

Sara




  1. It is possible that the four persons in the sample would all be females.

  2. It is possible that the sample would have two males and two females.

  3. The random sample of four persons will accurately represent the important features of the entire group.

  4. Each person in the group has an equal chance of being selected.

Answers:


  1. True

  2. True

  3. False

  4. True


Exercise 4
The second and third lines from Table H Random Numbers are shown below. Use these numbers to complete the random assignment of 18 subjects to three different experimental treatment conditions: 1, 2, 3. Assign subjects in blocks of three so that there will be equal numbers of subjects in each condition. Subject 1 is assigned to condition 3, subject 2 is assigned to condition 2, and then subject 3 is assigned by default to condition 1. Subject 4 is assigned to condition 2, subject 5 is assigned to condition 3, and subject 6 is assigned by default to condition 1, and so on.
37542 04805 64864 74296 24805 24037 20636 10402 00822 91665

08422 68953 19645 09303 23209 02560 15953 34764 35080 33606




Subj. No.

Condition



Subj. No.

Condition



Subj. No.

Condition



1

3

7




13




2

2

8




14




3

1

9




15




4

2

10




16




5

3

11




17




6

1

12




18



Answers:



Subj. No.

Condition



Subj. No.

Condition



Subj. No.

Condition



1

3

7

2

13

2

2

2

8

3

14

1

3

1

9

1

15

3

4

2

10

1

16

2

5

3

11

2

17

3

6

1

12

3

18

1


Exercise 5

The weight distribution of the 80 Pittsburgh Steelers team members is shown below. Source: http://www.steelers.com/team/player/




Lbs.

Frequency

340-359

2

320-339

6

300-319

8

280-299

8

260-279

4

240-259

9

220-239

13

200-219

14

180-199

15

160-179

1




    1. If you randomly select one player, what is probability that the player weighs between 300 lbs. and 319 lbs.?

    2. If you randomly select one player, what is the probability that the player weighs less than 200 lbs.?

    3. If you randomly select one player, what is the probability that the player weighs 300 lbs. or more?

    4. If you randomly select one player, what is the probability that the player weighs more than 339 lbs. or less than 180 lbs.?

Answers:



  1. 8/80 = .1

  2. 16/80 = .2

  3. 16/80 = .2

  4. 2/80 + 1/80 = 3/80 = .0375


Exercise 6
Tom has applied to the graduate programs of two universities: University A and University B. Let’s say that probability that Tom will be accepted at University A is .60 and the probability that Tom will be accepted at University B is .35. Assume that the acceptance decisions are independent of one another. What is the probability that


  1. Tom will be accepted at both University A and University B?

  2. Tom will be accepted at University A but not University B?

  3. Tom will be accepted at University B but not University A?

Answers:



  1. .60 × .35 = .21

  2. .60 × .65 = .39

  3. .35 × .40 = .14


Exercise 7
A small college reports that 55% of the student athletes on its campus are females. The college also says that 32% of its athletes are on a basketball team and 23% of its athletes are tennis players.


  1. The conditional probability that an athlete is a tennis player, given that the athlete is a female is 25%. If you randomly select one student athlete, what is the probability that the athlete is a female tennis player?

  2. The conditional probability that an athlete is a basketball player, given that the athlete is a male is 30%. If you randomly select one student athlete, what is the probability that the athlete is a male basketball player?

  3. The conditional probability that the athlete is neither a tennis player nor a basketball player, given that the athlete is a female is 42%. If you randomly select one student athlete, what is the probability that the athlete is a female who plays a sport other than tennis or basketball?




  1. .55 × .25 = .14

  2. .45 × .30 = .14

  3. .55 × .42 = .23


Exercise 8
Referring to the standard normal table (Table A, Appendix C), find the probability that a randomly selected z score will be


  1. below -1.96

  2. above 2.58

  3. between -2.58 and 2.58

Answers:



  1. .025

  2. .0049

  3. .4951 × 2 = .9902



Exercise 9
Hayhoe, Leach, Turner, Bruin, and Lawrence (2000) investigated differences between men and women college students with respect to their credit card use. Research participants completed a questionnaire that asked questions about the number of credit cards they had, attitudes toward credit purchases, types of items purchased with credit cards, financial practices, and so on. The table shown below presents a cross-tabulation of the participants’ gender by number of credit cards they said they had.


Gender

0 Cards

1-3 Cards

4 or More Cards

Female

36

141

94

Male

60

94

50




  1. If you randomly select one of these college students, what is the probability that the student has 0 credit cards given that the student is a male?

  2. If you randomly select one of these college students, what is the probability that the student is a female given that the student has 0 credit cards?

  3. If you randomly select two students, what is the probability that the second student is a male given that the first student was a female?

  4. If you randomly select two students, what is the probability that the second student is a female with 4 or more cards given that the first student was a female with 1-3 credit cards?

  5. If you randomly select three students, what is the probability that all three students have 4 or more credit cards?

Answers:


  1. 60/204 = .294

  2. 36/96 = .375

  3. (271/475)(204/474) = .246

  4. (141/235)(94/144) = .392

  5. (144/475)(143/474)(142/473) = .027


Exercise 10
Which of the following probability tests would be good candidates for the application of the Multiplication Rule?
The probability that …

  1. A flipped coin will be heads or tails.

  2. Incidences of infectious disease were diagnosed as idiopathic and occurring in Taos, New Mexico

  3. In a group of 35 people containing 10 men and 25 women, one individual chosen at random would be male

  4. When surveying a random selected sample from a population, one of the respondents will have been convicted of a crime

  5. When surveying faculty of one college, one of the respondents will have been convicted of a crime given the faculty member is male

  6. When clicking on the Wikipedia random article link, the article will be about statistical methods

  7. When clicking on the Wikipedia random article link twice, both of the articles will be about birds, assuming that the random page generator does not pick the same page twice

Answers: b, e, and g


Exercise 11
A professor has a weekly lecture class with a total of 72 students. The class has an equal number of men and women. The professor asks the teaching assistant to select students at random to participate in class demonstrations. Round your answers to two decimal places.


  1. If two students are chosen, what are the chances that both are men?

  2. If six students are chosen, how likely is it that the first four are women?

  3. If three students are chosen, what is the probable occurrence of all being men?

  4. If the ratio of women to men was two to one instead, what is the probability of three women being chosen?

Answers:



  1. (36/72)(35/71) = .25

  2. (36/72) (35/71)(34/70)(33/69) = .06

  3. (36/72)*(35/71)*(34/70) = .12

  4. (48/72)*(47/71)*(46/70) = .29


Exercise 12
In a university class, 30 students are psychology majors, 40 are sociology majors, 28 are psychobiology majors, and 2 are home economics majors. Each major has equal numbers of males and females. Round your answers to two decimal places except where noted.


  1. If two students are randomly selected, what is the probability that both are majoring in psychobiology?

  2. If one student is randomly selected, what is the probability that the student is a male given that the student is a home economics major?

  3. If three sociology majors are randomly selected, what is the probability that all will be males?

  4. If one student is randomly selected from the entire class roster, what is the probability that the student will be both a female and a sociology major?

  5. If four students are randomly selected, what is the probability that all will be either psychology or psychobiology majors given that all are females?

  6. If three students are randomly selected from the entire class roster, what is the probability that the first two will be female psychobiology majors and the third will be a male psychology major? Round the answer to three decimal places.

Answers:



  1. (28/100) (27/99) = .08

  2. (1/2) = .50

  3. (20/40) (19/39) (18/38) = .12

  4. (20/100) = .20

  5. (29/50) (28/49) (27/48) (26/47) = .10

  6. (14/100) (13/99) (15/98) = .003


Exercise 13
Between January 2000 and August 2013, there were 667 arrests of National Football League (NFL) players as reported by Union-Tribune News of San Diego. The table below presents the actual number of arrests of NFL players from January 2010 to December 2012. For this exercise, we will limit the total number of NFL players to 1,696. In addition, we will assume that no player was arrested more than once over the three-year period.

(Source: http://www.utsandiego.com/nfl/arrests-database/?appSession=

18370139710271&RecordID=&PageID=2&PrevPageID=&cpipage=3&CPISortType=&CPIorderBy=)


Year

Total number of arrests out of a total of 1,696 players

Number of cornerbacks arrested out of 64

Number of defensive ends arrested out of 64

Number of linebackers arrested out 64

2010

54

6

5

8

2011

48

7

6

6

2012

45

4

3

7

Randomly select players as instructed and calculate probabilities using the data in the table. Round answers to two decimal places unless otherwise instructed.




  1. If you randomly select a 2010 linebacker, what is the probability that the linebacker had been arrested?

  2. If you randomly select three NFL players from the combined pools of cornerbacks and defensive ends, how likely is it that two will be cornerbacks?

  3. Let's say that you choose two players at random from all players arrested in 2011. What are the chances that both players will be cornerbacks?

  4. If you randomly select two 2010 linebackers, what is the probability that both had been arrested? What is the probability of this same outcome for 2011? What is the probability of this same outcome for 2012?

  5. If you randomly select two players from the combined pool of all cornerbacks, defensive ends, and linebackers arrested during the three-year period, what is the probability that your first selection is a linebacker arrested in 2010 and your second selection is a defensive end arrested in 2011? Round the answer to three decimal places.

Answers:



  1. 8/64 = .13

  2. (64/128) (63/127) (64/126 = .13

  3. (7/48) (6/47) = .02

  4. 2010: (8/64) (7/63) = .01

2011: (6/64) (5/63) = .01

2012: 7/64) (6/63) = .01



  1. (8/129) (6/128) = .003


Exercise 14
Gallup’s annual poll of Consumption Habits asked U.S. adults who drink alcohol to identify their preferred beverage. The 2013 poll found that, among U.S. adults 18-29 years of age, 41% preferred beer, 24% preferred wine, and 28% preferred liquor. The questions that follow refer to the results obtained for adults 18-29 years of age. When answering the questions, assume that the events are independent. Round your answers to two decimal places.

Source: http://www.gallup.com/poll/163787/drinkers-divide-beer-wine-favorite.aspx




  1. If you randomly sample two poll participants, what is the probability that both prefer beer?

  2. If you randomly sample two poll participants, what is the probability both prefer liquor?

  3. If you randomly sample three participants, what is the probability that one prefers beer, one prefers wine, and one prefers liquor?

Answers:


  1. (.41) (.41) = .17

  2. (.28) (.28) = .08

  3. (.41) (.24) (.28) = .03


Reference
Hayhoe, C. R., Leach, L. J., Turner, P. R., Bruin, M. J., & Lawrence, F. C. (2000). Differences in spending habits and credit use of college students. The Journal of Consumer Affairs, 34, 113-133.





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