Section 1.1

Building Basic Skills and Vocabulary

1. How is a sample related to a population?
A sample is a subset of a population.

3. What is the difference between a parameter and a statistic?
A parameter is a numerical description of a population; a statistic is a numerical description of a sample.

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

5. A statistic is a measure that describes a population characteristic.
False; a statistic is a measure that describes a sample characteristic

7. It is impossible for the Census Bureau to obtain all the census data about the population of the United States.
True

9. A population is the collection of some outcomes, responses, measurements, or counts that are of interest.
False, t is a collection of ALL outcomes, etc

Classifying a Data Set In Exercises 11–16, determine whether the data set is a population or a sample. Explain your reasoning.

11. The age of each member of the House of Representatives
Population; collection of ages of all members of the House

13. A survey of 500 spectators from a stadium with 42,000 spectators
Sample; collection of 500 spectators is a subset within population of 42,000 spectators

15. The cholesterol levels of 20 patients in a hospital with 100 patients
Sample; collection of 20 patients is a subset within the population of 100 patients

Graphical Analysis In Exercises 17–20, use the Venn diagram to identify the population and the sample.

17. Population: Party of registered voters in Warren County
Sample: Party of registered voters who responded to phone survey

19. Population: ages of adults in the U.S. who own computers Sample: Ages of adults in the U.S. who own Dell computers

Using and Interpreting Concepts
Identifying Populations and Samples In Exercises 21–28, identify the population and the sample.

21. A survey of 1000 adults in the United States found that 12% prefer to take their vacation during the winter months.
Population: collection of adults in the United States
Sample: collection of 1000 adults in the survey

23. A survey of 1906 households in the United States found that 13% have a high definition television.
Population: collection of households in the United States
Sample: collection of 1906 households in the survey

25. A survey of 1045 registered voters found that 19% think the economy is the most important issue to consider when voting for Congress.
Population: collection of registered voters in the United States
Sample: collection of 1045 registered voters in the survey

27. A survey of 546 women found that more than 56% are the primary investor in their household.
Population: collection of women in the United States
Sample: collection of 546 women in the survey

Distinguishing Between a Parameter and a Statistic In Exercises 29–36, determine whether the numerical value is a parameter or a statistic. Explain your reasoning.

29. The average annual salary for 35 of a company’s 1200 accountants is $68,000.
Statistic; $68,000 is a numerical description of a sample of annual salaries

31. Sixty-two of the 97 passengers aboard the Hindenburg airship survived its explosion.
Parameter; 62 is a numerical description of a population of passengers

33. In a survey of a sample of computer users, 8% said their computer had a malfunction that needed to be repaired by a service technician.
Statistic; 8% is a numerical description of a sample of computer users

35. In a recent survey of 1503 adults in the United States, 53% said they use both a landline and a cell phone.
Statistic; 53% is a numerical description of a sample of adults

37. Which part of the survey described in Exercise 27 represents the descriptive branch of statistics? Make an inference based on the results of the survey.
“…56% are the primary investor in their household” represents descriptive statistics. An inference is that an association exists between women in the U.S. and being the primary investor in their household.

Section 1.2

Building Basic Skills and Vocabulary

1. Name each level of measurement for which data can be qualitative.
Nominal & ordinal

2. Name each level of measurement for which data can be quantitative.
Ordinal, interval & ratio

True or False? In Exercises 3–6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

3. Data at the ordinal level are quantitative only.
False; ordinal can also be qualitative

4. For data at the interval level, you cannot calculate meaningful differences between data entries.
False; interval allows for calculating meaningful differences

5. More types of calculations can be performed with data at the nominal level than with data at the interval level.
False; nominal is qualitative data, which cannot be calculated

6. Data at the ratio level cannot be put in order.
False; data at the ratio level can be put in meaningful order

Classifying Data by Type In Exercises 7–12, determine whether the data are qualitative or quantitative.

7. The telephone numbers in a telephone directory
Qualitative; they are just labels

8. The daily high temperatures for the month of July
Quantitative; they are numerical measures

9. The lengths of songs on an MP3 player
Quantitative; they can be sorted

10. The player numbers for a soccer team
Qualitative; they are just labels

11. Responses on an opinion poll
Qualitative; they are just responses, not numerical

12. Measure of diastolic blood pressure
Quantitative; they are numerical values

Using and Interpreting Concepts
Classifying Data by Level In Exercises 13–18, determine whether the data are qualitative or quantitative and identify the data set’s level of measurement. Explain your reasoning.

13. Football The top five teams in the final college football poll released in January 2007 are listed.
1. Florida 2. Ohio State 3. LSU 4. USC 5. Boise State
Ordinal; they can be put in order, but no calculations can be performed

14. Politics The three political parties in the 110th Congress are listed below.
Republican Democrat Independent
Nominal; they are just labels, there is no order or calculation that can be done

15. Top Salesperson The region representing the top salesperson in a corporation for the past six years is given.
Southeast Northwest Northeast
Southeast Southwest Southwest
Nominal; they are just labels and can be categorized, but differences are not meaningful

16. Fish Lengths The lengths (in inches) of a sample of striped bass caught in
Maryland waters are listed.
16 17.25 19 18.75 21 20.3 19.8 24 21.82
Ratio; they can be ordered, data values can be subtracted and values are multiples of one another

17. Best Seller List The top five hardcover fiction books on The New York Times
Best Seller List on February 21, 2007 are shown.
1. Step on a Crack 2. Plum Lovin’ 3. Natural Born Charmer 4. High Profile 5. Hannibal Rising
Ordinal; labels that can be categorized but no data calculations

18. Ticket Prices The average ticket prices for 10 rock concerts in 2005 are listed.
$134 $104 $55 $63 $76 $38 $35 $81 $47 $97
Ratio; data values can be subtracted and values are multiples of one another

Graphical Analysis In Exercises 19–22, identify the level of measurement of the data listed on the horizontal axis in the graph.

19. Nominal; opinion responses are merely labels

20. Ratio; snowfall average can have differences in data and values are multiples of one another

21. Nominal; genders are merely labels

22. Interval; differences in data can be calculated but values are not multiples of one another

23. The following appear on a physician’s intake form. Identify the level of measurement of the data.
a. Temperature b. Allergies c. Weight d. Pain level (scale of 0 to 10)
a. Interval b. Nominal c. Ratio d. Ratio

1.3

Building Basic Skills and Vocabulary

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

9. The method for selecting a stratified sample is to order a population in some way and then select members of the population at regular intervals.
False; this is the systematic sample. Stratified includes members from each segment of the population.

Deciding on the Method of Data Collection In Exercises 11–14, decide which method of data collection you would use to collect data for the study. Explain.

11. A study of the effect on the human digestive system of potato chips made
Experiment; allow subjects to eat the potato chips to gather data

13. A study of how fast a virus would spread in a metropolitan area
Simulation; too dangerous to carry out such a method in real life

Using and Interpreting Concepts

15. Allergy Drug A pharmaceutical company wants to test the effectiveness of a new allergy drug. The company identifies 250 females 30–35 years old who suffer from severe allergies. The subjects are randomly assigned into two groups. One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug. After six months, the subjects’ symptoms are studied and compared.

(a) Identify the experimental units in this experiment.
Females ages 30-35
(b) How many treatments are used in this experiment?
One treatment, one placebo
(c) Identify a potential problem with the experimental design being used and suggest a way to improve it.
Members are all female as drug could have different affects depending on sex
(d) How could this experiment be designed to be double-blind?
Allow another party to administer the drug and placebo without the experimenter’s intervention or knowing.

Identifying Sampling Techniques In Exercises 17–26, identify the sampling technique used and discuss potential sources of bias (if any). Explain.

17. Using random digit dialing, researchers called 1599 people and asked what obstacles (such as childcare) kept them from exercising.
Simple random sample; every member of the sample have an equal chance of being selected

19. Questioning students as they left a university library, a researcher asked 358 students about their drinking habits.
Convenience sample; students chosen due to their convenience of location

21. Chosen at random, 1210 hospital outpatients were contacted and asked their opinion of the care they received.
Simple random sample; patients all have equal chance of being selected

23. Soybeans are planted on a 48-acre field. The field is divided into one-acre subplots. A sample of plants is taken from each subplot to estimate the harvest.
Stratified sample; plants from each segment of the population are selected

25. A list of managers is compiled and ordered. After a starting number is randomly chosen, every ninth name is selected until 1000 managers are selected. The managers are questioned about the use of digital media.
Systematic sample; managers are selected at an interval

27. Sleep Deprivation A researcher wants to study the effects of sleep deprivation on motor skills. Eighteen people volunteer for the experiment: Jake, Maria, Mike, Lucy, Ron, Adam, Bridget, Carlos, Steve, Susan, Vanessa, Rick, Dan, Kate, Pete, Judy, Mary, and Connie. Use a random number generator to choose 9 subjects for the treatment group. The other 9 subjects will go into the control group. List the subjects in each group. Tell which method you used to generate the random numbers.
Systematic sample; start at 2, pick every 3rd member.

Choosing between a Census and a Sampling In Exercises 29 and 30, determine whether you would take a census or use a sampling. If you would use a sampling, decide what sampling technique you would use. Explain your reasoning.

29. The average salary of the 50 employees of a company
Census; 50 is a small number so it is easier to get everyone’s numbers

Recognizing a Biased Question In Exercises 31–34, determine whether the survey question is biased. If the question is biased, suggest a better wording.

31. Why is drinking fruit juice good for you?
Biased; assumes fruit juice is good for you. “Is drinking fruit juice good for you?”

33. How many hours of sleep do you get on an average night?
Not biased

35. Writing Television program ratings by Nielsen Media Research are described on page 17. Discuss the strata used in the sample.
Tracks patterns of 10,000 households in the population with various attributes

Extending Concepts

37. Open and Closed Questions Two types of survey questions are open questions and closed questions. An open question allows for any kind of response; a closed question allows only for a fixed response. An open question and a closed question with its possible choices are given below. List an advantage and a disadvantage of an open question. Then list an advantage and a disadvantage of a closed question.

Open Question
Advantage: allows depth and shades of meaning to an answer
Disadvantage: Not easily quantified and difficult to compare surveys

Closed
Advantage: easy to analyze results
Disadvantage: may not provide alternatives and influence opinions of respondent
39. Give an example of an experiment where confounding may occur.
A coffee shop has a promotion to bring in more customers. At the same time, a new record store opens next door. The coffee shop cannot determine if the new customers are pulled from the record store or from the promotion.

41. How are the placebo effect and Hawthorne effect similar? How are they different?
They are similar in that the participants know they are subjects of a test. A placebo affect is when a subject acts favorably to a placebo when in actuality no medicated treatment took place. The Hawthorne effect takes place when a subject reacts in a certain way simply because they know they are being watched.

43. Using Sampling Techniques You have been asked by your school to survey 150 students who use the new fitness center. Describe your procedure for obtaining a sample of each type: random, stratified, cluster, systematic, and convenience.