Section 1.1 Exercises

Chapter: 1 Basic Ideas

SECTION 1.1 EXERCISES

Understanding the Concepts

Exercises 1-6 are the Check Your Understanding exercises located within the section. Their answers are found on page 12.

7. population

8. sample

9. simple random sample

10. sample of convenience

11. cluster

12. stratified

13. False. A sample of convenience is acceptable when it is difficult or impossible to draw a sample in a truly random way.

14. False. In a cluster sample, a simple random sample of clusters is selected, and every individual in each selected cluster is part of the sample.

15. True.

16. True.

Practicing the Skills

17. Statistic

18. Parameter

19. Parameter

20. Statistic

21. Answers will vary.

22. Answers will vary. Stratified

23. Answers will vary. Cluster

24. Answers will vary. Systematic

25. Stratified

26. Cluster

27. Sample of convenience

28. Systematic

29. Voluntary response

30. Cluster

31. Sample of convenience

32. Simple random sample

33. Stratified

34. Cluster

35. Simple random sample

36. Stratified

Working with the Concepts

37. Sample of convenience. In order to choose a simple random sample, every individual in the population has to have the same chance of being selected. Since presumably every person in the world suffers from headaches, this means that the pharmaceutical company would have to randomly select persons from every state and every country, which is not feasible.

38. Simple random sample. It would not be difficult to randomly select 100 students from all of the student body at a university. Each student has a student ID number and 100 students could be randomly selected from them via a lottery type generator.

39. Obtain a list of all registered voters in the town, and randomly select out 500 of them.

40. Randomly choose items off of the assembly line. For instance, take an item. Then maybe let 10 go by, then take another item. Let 10 more go by, then select another item. Let 10 more go by, select another item. Continue selecting items in this fashion.

41. Draw a stratified sample. That is, separate the employees by gender, then randomly choose equal number of men and women from their respective strata.

42. Using a computer, the IRS can randomly select 1000 W2 tax forms from the population of all tax forms.

Extending the Concepts

43. To get a simple random sample,

we could have the school’s admission’s office randomly choose 75 names from the entire student enrollment, then we would interview these subjects. To get a sample of convenience, we could go to the school’s student center and randomly ask students about their opinions. We could put an advertisement in the school’s newspaper, or hand out flyers on campus,asking students to go to a particular Facebook page and express their opinions on the issue. This would be an example of voluntary response sampling. If we have the school’s admission’s office draw a simple random sample of 50 males at the school, as well as a simple random sample of 50 females at the school, and we interview all subjects within these two strata, this would be stratified sampling. If we choose three different one-half hour time intervals, and interview all students at the library as to their opinion on the issue, this would be an example of cluster sampling. Finally, if we interview every 8th student that walks into the library over a certain amount of time, this wouldbe an example of systematic sampling.

44. In cluster sampling, the population is

divided into clusters, then a simple random sample of these clusters is selected, and every unit within the selected clusters is sampled. This is a two-stage sampling plan. In systematic sampling, we first select a random starting point in the population,and then sample every kthitem beginning at that starting point. This is also a two-stage sampling plan, where we employ a simple random sample of size 1 from the list of potential starting points, and then census the sampling units at multiples of k units from the initial unit.

SECTION 1-2 EXERCISES

Understanding the Concepts

Exercises 1-4 are the Check Your Understanding exercises located within the section. Their answers are found on page 18.

5. variables

6. qualitative

7. Quantitative

8. nominal; ordinal

9. discrete

10. Continuous

11. False. Quantitative variables do.

12. True

13. True

14. True

Practicing the Skills

15. qualitative

16. quantitative

17. quantitative

18. qualitative

19. quantitative

20. quantitative

21. qualitative

22. qualitative

23. qualitative

24. quantitative

25. ordinal

26. nominal

27. ordinal

28. ordinal

29. nominal

30. nominal

31. nominal

32. ordinal

33. continuous

34. continuous

35. discrete

36. discrete

37. continuous

38. discrete

Working with the Concepts

39. ordinal

40. discrete

41. ordinal

42. quantitative

43. nominal

44. ordinal

45(A) Game Title and Publisher

(B) % of Gaming Audience and

Average Minutes Played per Week

(D) Game Title

46(A) Movie Title, Creative Type,

and MPAA Rating

(B) Year, Ticket Sales, and Tickets Sold

(D) MPAA Rating

Extending the Concepts

47(A) ordinal

(B) yes

(D) quantitative

(E) yes; yes

(F) nominal

(G) no; no

SECTION 1-3 EXERCISES

Understanding the Concepts

Exercises 1-4 are the Check Your Understanding exercises located within the section. Their answers are found on page 26.

5. randomized

6. double-blind

7. observational

8. confounder

9. prospective

10. cohort

11. True

12. False. A confounder makes it harder to draw conclusions from a study.

13. False. In an observational study, subjects choose their own treatments.

14. False. Observational studies are generally less reliable than randomized experiments.

15. True

16. True

Practicing the Skills

17(A) It is a randomized experiment.

(B) Yes. In a randomized experiment, if

there are large differences in outcomes among the treatment groups, we may conclude that the differences are due to the treatments.

18(A) It is an observational study.

(B) No. In an observational

study, when there are differences in the outcomes among the treatment groups, it is often difficult to determine whether the differences are due to the treatments or to confounding.

19(A) It is a randomized experiment.

(B) Yes. In a randomized experiment, if

there are large differences in outcomes among the treatment groups, we may conclude that the differences are due to the treatments.

20(A) The four types of fertilizer.

(B) It is a randomized experiment.

there are large differences in outcomes among the treatment groups, we may conclude that the differences are due to the treatments.

Working with the Concepts

21. An observational study will be

necessary, this is because the subjects themselves decide where they live.

22. It is possible to design a

randomized experiment, since the scientists may assign the subjects at random to the two treatments.

23. It could be due to confounding.

24. It could be due to confounding.

25(A) False

(B) True

26. Age is a likely confounder.

Older children tend to be taller and also tend to know more words.

27(A) heart rate

(B) maternal smoking

(D) prospective

(E) Yes. Smoking mothers may be in worse shape than nonsmoking mothers, and the conditioning (or lack thereof) may be a confounder.

28(A) respiratory problems

(B) formaldehyde level

(D) cross-sectional

(E) it is unlikely

Extending the Concepts

29(A) yes

(B) It was important for the doctors in the study not to know which children were getting the vaccine because a doctor’s diagnosis may be influenced by the knowledge of which particular treatment a patient received.

30(A) no

(B) no

(C) It could still be due to confounding of one’s socio-economic status. Again, the children who did not participate in the study were more likely to come from lower-income families, who tended to have lower rates of polio.

SECTION 1-4 EXERCISES

Understanding the Concepts

Exercises 1 and 2 are the Check Your Understanding exercises located within the section. Their answers are found on page 29.

3. voluntary response surveys

4. nonresponders

5. population

6. False. The way that a question in a survey is worded has a huge effect on the responses.

7. True

8. False. The fact that a sample is large, doesnot make it any better or more reliable.

Practicing the Skills

9. nonresponse

10. sampling bias

11. self-interest

12. nonresponse

13. voluntary response

14. social acceptability

15. nonresponse

16. social acceptability

Working with the Concepts

17(A) No.

(B) No. The first survey has self-interest bias, and the second one has social acceptability as well as leading question bias.

18. Yes, because many people do

not pick up the phones when they do not recognize the number ontheir caller ID. This creates nonresponse bias.

19. Yes, because many people have

gone completely cellular, and such a sampling method misses this entire large group of people.

20. Yes, many people pick the first of

something when they are not sure.

Extending the Concepts

21(A) In essence, the poll surveyed

the rich, and a majority of the rich are Republicans. That is why, the digest had the Republican candidate incorrectly winning in a landslide.

(B) Only about one-fifth of the

surveys were returned. This creates

nonresponse bias.

offset bias.

Chapter Quiz

1. Answers will vary.

2. qualitative

3. True

4. Continuous

5. False. It should represent the

population as much as possible.

6. stratified sample

7. acceptable

8. sample of convenience

9. True

10. observational study

11. randomized experiment

12. differences in the treatments

13. Seniors are older and maybe better prepared and more experienced.

14. True

15. Not reliable at all.

Review Exercises

1. quantitative

2. nominal

3. continuous

4(A) True

(B) True

5. stratified sample

6. voluntary response sample

7. cluster sample

8. simple random sample

9. (A) observational study

(B) Yes, people in countries with

the fluoridation of water are probably wealthier than people in countries without it, and therefore probably have better overall dental care.

10(A) randomized experiment

(B) It is unlikely, because in a

randomized experiment, if there are large differences in outcomes among the treatment groups, we may conclude that the differences are due to the treatments.

11(A) observational study

(B) Yes, because in an

observational study, when there are differences in the outcomes among the treatment groups, it is often difficult to determine whether the differences are due to the treatments or to confounding.

12(A) randomized experiment

(B) It is unlikely, because in a

randomized experiment, if there are large differences in outcomes among the treatment groups, we may conclude that the differences are due to the treatments.

13. It is a voluntary response

sample.

14. It has nonresponse bias.

15. It has nonresponse bias.

Write About It

1. A stratified sample is one in

which the population is divided into groups and a random sample is drawn from each group. In a cluster sample, a simple random sample of clusters is selected, and every individual in each selected cluster is part of the sample.

2. The most basic, and in many

cases the best, sampling method is the method of simple random sampling. In simple random sampling, the sample represents the population very closely. This is very desirable. However, in a sample of convenience, the sample may differ systematically in some way from the population.

3. A circumstance under which a

sample of convenience might be used is when an engineer wishes to study the crushing strength of a hugh shipment of concrete blocks that are very heavy. In such an instance, sampling blocks in the center or on the bottom might not be possible.

A cluster sample would be used to estimate the unemployment rate in a county. In this instance, a simple random sample of households in the county would be selected, and every member of each household would be interviewed.

A stratified sample would be used if we wanted to poll the opinions on a certain issue by gender. The population would be divided into the two genders, and a random sample would be selected out of each sex.

A systematic sample is employed

when police pull over every 10th car or so at a sobriety check point.

Whenever possible, we prefer to use a simple random sample selected from a population of interest.

The governing principle here is that each subject has the same likelihood of being selected for the sample. Any method of selecting the subjects (like randomly generating a list of names from a computer random number generator) that is analogous to lottery selection, works fine.

4. An example of an ordinal random

variable is X = the letter grade on exam #1 for each student in the statistics class

An example of a nominal random variable is X = the political part affiliations of all the students in the class

An example of a discrete random variable is X = the number of people who went to the mall today

An example of a continuous random variable is X = the weights (in pounds) of all the students in the class

5. Qualitative variables are not

numeric. They are variables that classify subjects into categories.

6. The major difference between a

randomized experiment and an observational study has to do with the nature of assigning the subjects to respective treatment groups. If the assignment is made by the investigator it is randomized. If however, the assignment is not made by the investigator, it is observational. As such, if there are large differences in outcomes among the treatment groups in a randomized study, we may conclude that the differences are attributed to the treatments. This is not necessarily true for an observational study because of the effects of confounding.

7. In a double-blind study, neither

the investigators nor the subjects know who has been assigned to which treatment. The major advantage to this is that no biases of the doctors or subjects can interfere with the results. There really is no disadvantage, other than it is not always possible to do such a study. However, whenever possible, double-blind studies should be performed.

8. If a major pharmaceutical

company pays a statistician a lot of money to perform statistical analyses as to the utility of a certain drug, the statistician has a paid vested interest in the outcome, as does the company. It might be tempting to “fudge” the results to obtain a positive outcome.

9(A) This question has very

leading question bias. It is hinting that people are doing something wrong and really should change. A better question would be, “If you had more money, do you think you would spend it or save it?”

(B) This question has social

acceptability bias. A much better question would be, “What is your opinion on funding for charitable organizations?” Chose from the following: they have enough, they need more, or they have too much

Case Study: Air Pollution and Respiratory Symptoms

1. 450

2. 41

3. 9.1%

4. 43

5. 2

6. 4.7%

7. Yes, there is a significant difference

between the two.

8. Because every person who

returned the questionnaire via school return did so on a day that corresponded to a high exposure PM level.

9. Because every person who

returned the questionnaire via mail return did so on a day that corresponded to a low exposure PM level.

10. The people who did not return

their questionnaires via school return, had to be mailed another questionnaire. This time delay caused the researchers to get these questionnaires later, well into April when it was warmer. Since less wood burning stoves are being used than they were in March, this definitely affects the PM level and wheezing percentages.

11. The people who had symptoms all returned their questionnaires via school return, with the exception of two who mailed it in. Everyone else who mailed in their responses did not have any symptoms. This is indeed evidence that people who have symptoms are eager to participate, while those who are unaffected are less interested. Therefore, the mode of response is related to the outcomes.

12. By telephoning the subjects over

a few days or weeks, the confounding would have been drastically reduced because then they would not have had the striking change in weather affecting the outcomes. Notice how the actual study went from March 5 until April 22.

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.