under study while a sample is a subgroup of

Chapter 1 - The Nature of Probability and Statistics 1 E

XERCISE SET 1-1

• Statistics is the science of conducting

studies to collect, organize, summarize, analyze, and draw conclusions from data.

• A variable is a characteristic or attribute

that can assume different values.

• In a census, the researchers collect data

from all subjects in the population.

• A population consists of all subjects

under study while a sample is a subgroup of the population.

• Descriptive statistics consists of the

collection, organization, summarization, and presentation of data while inferential statistics consists of generalizing from samples to populations, performing estimations and hypothesis testing, determining relationships among variables, and making predictions.

• Probability is used in gambling,

insurance, and weather forecasting.

• Samples are used more than populations

both because populations are usually large and because researchers are unable to use every subject in the population.

• A biased sample is a sample that is not

representative of the population.

• This is inferential because a

generalization is being made about the population.

• This is inferential since a prediction is

being made about the future.

• This is a descriptive statistic.
• This is a descriptive statistic since it is

based on the results of a survey of 2739 individuals. However, if an inference were made to all pet owners, it would be an inferential statistic.

• This is an inferential statistic since a

generalization about the population is being made.

• This is a descriptive statistic.
• This is a descriptive statistic since it is

based on an online survey of 500 students.

• This is a descriptive statistic.
• This is an inferential statistic since it is a

generalization made from data obtained from a sample.

• Answers will vary.
• Answers will vary.

EXERCISE SET 1-2

• Qualitative variables are variables that

can be placed in distinct categories according to some characteristic or attribute and cannot be ranked; while quantitative variables are numerical in nature and can be ordered or counted.

• Discrete variables assume values that can

be counted while continuous variables are variables obtained by being measured.Theoretically, continuous variables can assume all values between any given two values.

• Continuous variables need to be rounded

because of the limits of the measuring device.

• There are four types of measurement

levels used in statistics: nominal, ordinal,

interval, and ratio levels of measurement.

• Qualitative 6. Quantitative
• Quantitative 8. Quantitative
• Qualitative 10. Quantitative
• Qualitative 12. Continuous
• Continuous 14. Discrete
• Discrete 16. Continuous
• 6.5-7.5 feet
• 6.25-6.35 millimeters

Elementary Statistics, A Step by Step Approach 9e Allan Bluman (Solutions Manual All Chapters, 100% Original Verified, A+ Grade) 1 / 4

Chapter 1 - The Nature of Probability and Statistics 2

• 142.5-143.5 miles
• 3.245-3.255 pounds
• 25.75-25.85 yards
• 18.5-19.5 quarts
• Nominal 24. Interval
• Ratio 26. Ratio
• Ordinal 28. Nominal
• Ratio 30. Ratio

EXERCISE SET 1-3

• Data can be collected by using telephone

surveys, mail questionnaire surveys, personal interview surveys, by taking a look at records, or by direct observation methods.

• Sampling error is the difference between

a sample measure and a population measure.Nonsampling error is the result of collecting data incorrectly or selecting a biased sample.

• Random numbers are used in sampling so

that every subject in the population has an equal chance of being selected for a sample.Random numbers can be generated by computers or calculators; however, there are other ways of generating random numbers such as using a random number table or rolling dice.

• The four basic sampling methods are

random, systematic, stratified, and cluster methods.

• The population could be all adults in the

United States. A sample could have been selected by a mail survey. Answers will vary.

• The population could be all automobiles

in the United States stolen during 2010. A sample could be obtained by looking at police records. Answers will vary.

• The population could be all pet owners in

the United States. A sample could be obtained by looking at veterinarians' records.However, these records would not include

• continued

pet owners who do not take their pets to veterinarians. Answers will vary.

• The population could be all adults in the

United States. A sample could be obtained by checking the blood levels of calcium. Of course, the researcher must be aware of the privacy rights of the respondents. Answers will vary.

• The population could be all adults in the

United States who develop diabetes during

• The sample could be surveying

patient records of these people to see if they have been taking statins. Again, the privacy rights must be considered. Answers will vary.

• The population could consist of all daily

temperatures in Boston since records were kept, and a sample could be obtained by looking at weather report statistics.

• Systematic 12. Stratified
• Random 14. Cluster
• Cluster 16. Random

EXERCISE SET 1-4

• In an observational study, the researcher

observes what it happening and tries to draw conclusions based on the observations. In an experimental study, the researcher manipulates one of the variables and tries to determine how this influences the variables.

• The three types of observational studies

are

• Cross-sectional studies in which the data

are collected at one point in time

• Retrospective studies in which the data

are collected from past records

• Longitudinal studies in which the data are

collected over a period of time

• One advantage of an observational study

is that it can occur in a natural setting. In addition, researchers can look at past instances of statistics and draw conclusions from these situations. Another advantage is that the researcher can use variables, such as drugs, that he or she cannot manipulate. 2 / 4

Chapter 1 - The Nature of Probability and Statistics 3

• continued

One disadvantage is that since the variable cannot be manipulated, a definite cause-and- effect situation cannot be shown. Another disadvantage is that these studies can be expensive and time-consuming. These studies can also be influenced by confounding variables. Finally, in these studies, the researcher sometimes needs to rely on data collected by others.

• One advantage of an experimental study

is that the researcher can decide how to select the subjects and assign them to the specific groups. The researcher can also control the independent variable. One disadvantage of an experimental study is that it may not occur in a natural setting.Another one is called the Hawthorne effect, and it is that the subject may change their natural behavior because they realize that they are participating in a research study.

• In an experimental study, the researcher

has control of the assignment of subjects to the groups whereas in a quasi-experimental study, the researcher uses intact groups.

• An independent variable is the one being

manipulated by the researcher whereas the dependent variable is the one being studied to identify the effects of the independent variable.

• In research studies, a treatment group

subject receives a specific treatment while those in the control group do not receive a treatment or are given a placebo.

• The Hawthorne effect was the effect

discovered when researchers realized that the workers at the Hawthorne plant knew that they were participating in a research study and this fact actually changed workers' behavior.

• A confounding variable is one that can

influence the results of the research study when no precautions were taken to eliminate it from the study.

• Sometimes subjects respond favorably

when given a placebo rather than the real treatment.

• Blinding is used to help eliminate the

placebo effect. Here the subjects are given a sugar pill that looks like the real medical pill. The subjects do not know which pill they are getting. When double blinding occurs, neither the subjects nor the researchers are told who gets the real treatment or the placebo.

• Randomized blocks are used to help

eliminate the Hawthorne effect and the placebo effect. Also they help to eliminate confounding variables since randomly assigning subjects to groups tends to "balance out" the inconsistencies (such as age, social class, etc.) that each of the subjects brings to the study.

• In a completely randomized design, the

subjects are assigned to the groups randomly, whereas in a matched-pair design, subjects are matched on some variable.Then one subject is randomly assigned to one group, and the other subject is assigned to the other group. In both types of studies, the treatments can be randomly assigned to the groups.

• When sample sizes are small,

replication of the study is done with larger groups to help rule out inconsistencies caused by a small group of subjects.

• Experimental
• Observational
• Observational
• Experimental
• Independent variable - minutes

exercising Dependent variable - catching a cold

• Independent variable - hugs and hand

holding Dependent variable - heart rate and blood pressure

• Independent variable - time spent in

meditation Dependent variable - rational decisions

• Independent variable - income 3 / 4

Chapter 1 - The Nature of Probability and Statistics 4

• continued

Dependent variable - number of times people visit a fast-food restaurant

• Age, income, socioeconomic status.

Answers will vary.

• Age, intelligence, family ties. Answers

will vary.

• Wealth, age, education. Answers will

vary.

• Climate, diet, medicine. Answers will

vary.

• How is a perfect body defined

statistically?

• What is meant by the "whole truth"?
• How can 24 hours of pain relief be

measured?

• How can reading a book increase a

person's IQ?

• How much weight, if any, will be lost?
• The stueps in conducting a medical

study are as follows:

Step 1. Formulate the purpose of the study.Step 2. Identify the variables for the study.Step 3. Define the population.Step 4. Decide what sampling method to use to collect the data.Step 5. Collect the data.Step 6. Summarize the data and perform any statistical calculations needed.Step 7. Interpret the results.

• Only 20 people were used in the study.
• The only time claims can be proved is

when the entire population is used.

• It is meaningless since there is no

definition of "the road less traveled." Also, there is no way to know that for 100every women, 91 would say that they have taken "the road less traveled."

• Since the results are not typical, the

advertisers selected only a few people for

• continued

whom the weight loss product worked extremely well.

• There is no mention of how this

conclusion was obtained.

• "74% more calories" than what? No

comparison group is stated.

• Since the word is used, there is nomay

guarantee that the product will help fight cancer.

• What is meant by "24 hours of acid

control"? Also implies that itcan provide might or might not provide control.

• No. There are many other factors that

contribute to criminal behavior.

42. Possible answer: It could be the amount

of caffeine in the coffee or tea. It could have been the brewing method.

• Answers will vary.
• Answers will vary.
• Answers will vary.
• Answers will vary.

REVIEW EXERCISES - CHAPTER 1

• Inferential 2. Descriptive
• Descriptive 4. Descriptive
• Inferential 6. Inferential
• Descriptive 8. Inferential
• Ratio 10. Ordinal
• Interval 12. Ratio
• Ratio 14. Ratio
• Ordinal 16. Ratio
• Ratio 18. Nominal
• Qualitative 20. Quantitative
• / 4