EXERCISE SET 1-1 - EXERCISE SET 1-1 1. Statistics is the science o...

Chapter 1 - The Nature of Probability and Statistics

EXERCISE 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.

11.This is a descriptive statistic since it describes the weight loss for a specific group of subjects, i.e. , the teenagers at Boston University.

12.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.

13.This is an inferential statistic since a generalization has been made about the population.

14.This is an inferential statistic since a generalization was made about the population of all kindergartens in the state of Oregon.

15.This is an inferential statistic since a generalization was made about the population.

16.This is a descriptive statistic since it describes the results of a specific survey of 1,507 subjects.

17.This is an inferential statistic since it is a generalization made from data obtained from a sample.

18.Answers will vary.

19.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.Copyright8©820188McGraw-Hill8Education.8 8All8rights8reserved.8No8reproduction8or8distribution8without8the8prior8written8consent8of8McGraw-Hill8Education8

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Chapter 1 - The Nature of Probability and Statistics 2.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.

3.Continuous variables need to be rounded because of the limits of the measuring device.

4.There are four types of measurement

levels used in statistics: nominal, ordinal,

interval, and ratio levels of measurement.

5.Qualitative 6. Qualitative

• Quantitative 8. Quantitative
• Discrete
• Discrete
• Quantitative 10. Qualitative

12.Continuous 13.Continuous 14. Discrete

• Continuous
• 23.5-24.5 feet
• 6.25-6.35 millimeters
• Nominal
• 142.5-143.5 miles
• 19.625-19.635 tons
• 200.65-200.75 miles
• 18.5-19.5 quarts
• Interval
• Ratio 26. Ratio
• Ordinal 28. Nominal

29.Ratio 30. Ratio

EXERCISE SET 1-3

1.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.

2.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.

3.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.

4.The four basic sampling methods are random, systematic, stratified, and cluster methods.

5.The population could be all people in the United States who earn over $200,000 per annum. A sample could have been created by selecting 500 people randomly from an accounting firm that prepares income taxes.Answers will vary.

6.The population could be all prisons in the free world. A sample of a specific number could be selected by randomly choosing prisons in the United States and prisons in other countries. Answers will vary.

7.The population could be all households in the United States. A sample could be selected using 1000 households in the United States.Answers will vary. Copyright8©820188McGraw-Hill8Education.8 8All8rights8reserved.8No8reproduction8or8distribution8without8the8prior8written8consent8of8McGraw-Hill8Education8

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Chapter 1 - The Nature of Probability and Statistics 8.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.

9.The population could be all adults in the United States who develop diabetes. 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.

10.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.

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

EXERCISE SET 1-4

1.In an observational study, the researcher observes what is 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 3.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.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.

4.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 which is when the subject may change their natural behavior because they realize that they are participating in a research study.

5.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.

6.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.

7.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.Copyright8©820188McGraw-Hill8Education.8 8All8rights8reserved.8No8reproduction8or8distribution8without8the8prior8written8consent8of8McGraw-Hill8Education8 3 Solutions Manual for Elementary Statistics A Step By Step Approach 10e Allan Bluman (All Chapters, 100% Original Verified, A+ Grade) 3 / 4

Chapter 1 - The Nature of Probability and Statistics 8.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.

• Randomization is 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.Copyright8©820188McGraw-Hill8Education.8 8All8rights8reserved.8No8reproduction8or8distribution8without8the8prior8written8consent8of8McGraw-Hill8Education8 4

• Replication is done to determine ifresults apply in different settings. Forexample, if the experiment was done withcollege students, the researchers mightreplicate the experiment with adults or inanother part of the country.
• Observational
• Observational
• Experimental
• Observational
• Independent variable - minutes

exercising Dependent variable - catching a cold

• Independent variable - hugs and hand

holding Dependent variable - heart rate and blood pressure

• Independent variable - happy face on

the check Dependent variable - amount of the tip

• Independent variable - marital status

Dependent variable - cause of death

• Age, income, socioeconomic status.

Answers will vary.

• Age, intelligence, family ties. Answers

will vary.

• Income, number of hours worked, type

of boss. Answers will vary.

• Climate, diet, medicine. Answers will

vary.

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