SOLUTIONS MANUAL - Chapter 2 Methods for Describing Sets of Data 6

SOLUTIONS MANUAL

NANCY S. BOUDREAU

A FIRST COURSE

IN STATISTICS

T

WELFTH EDITION

James McClave Terry Sincich By 1 / 4

TABLE OF CONTENTS

Chapter 1: Statistics, Data, and Statistical Thinking 1

Chapter 2 Methods for Describing Sets of Data 6 Chapter 3 Probability 48 Chapter 4 Random Variables and Probability Distributions 73

Chapter 5 Inferences Based on a Single Sample: Estimation with Confidence 125

Intervals

Chapter 6 Inferences Based on a Single Sample: Tests of Hypothesis

154 Chapter 7 Comparing Population Means 194 Chapter 8 Comparing Population Proportions 242 Chapter 9 Simple Linear Regression

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Statistics, Data, and Statistical Thinking 1

Copyright © 2017 Pearson Education, Inc.Statistics, Data, and Statistical Thinking

1.2 Descriptive statistics utilizes numerical and graphical methods to look for patterns, to summarize, and to present the information in a set of data. Inferential statistics utilizes sample data to make estimates, decisions, predictions, or other generalizations about a larger set of data.

1.4 The first major method of collecting data is from a published source. These data have already been collected by someone else and is available in a published source. The second method of collecting data is from a designed experiment. These data are collected by a researcher who exerts strict control over the experimental units in a study. These data are measured directly from the experimental units. The third method of collecting data is from a survey. These data are collected by a researcher asking a group of people one or more questions. Again, these data are collected directly from the experimental units or people. The final method of collecting data is observationally. These data are collected directly from experimental units by simply observing the experimental units in their natural environment and recording the values of the desired characteristics.

1.6 A population is a set of existing units such as people, objects, transactions, or events. A variable is a characteristic or property of an individual population unit such as height of a person, time of a reflex, amount of a transaction, etc.

1.8 A representative sample is a sample that exhibits characteristics similar to those possessed by the target population. A representative sample is essential if inferential statistics is to be applied. If a sample does not possess the same characteristics as the target population, then any inferences made using the sample will be unreliable.

1.10 Statistical thinking involves applying rational thought processes to critically assess data and inferences made from the data. It involves not taking all data and inferences presented at face value, but rather making sure the inferences and data are valid.

1.12 a. High school GPA is a number usually between 0.0 and 4.0. Therefore, it is quantitative.

• High school class rank is a number: 1st, 2nd, 3rd, etc. Therefore, it is quantitative.

• The scores on the SAT's are numbers between 200 and 800. Therefore, it is

quantitative.

• Gender is either male or female. Therefore, it is qualitative.

• Parent's income is a number: $25,000, $45,000, etc. Therefore, it is quantitative.

f. Age is a number: 17, 18, etc. Therefore, it is quantitative.

1.14 a. The experimental unit for this experiment is a drafted NFL quarterback.

• Draft position is one of three categories. Therefore, it is a qualitative variable. NFL

winning ratio is a number. Therefore, it is a quantitative variable. QB production score is a number. Therefore, it is a quantitative variable.Chapter

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• Chapter 1

Copyright © 2017 Pearson Education, Inc.

• Because all quarterbacks drafted over a 38-year period were used, the application of this

study is descriptive statistics.

1.16 a. The variable “difference between before and after sprint times” is measured in seconds.Thus, it is quantitative. The variable “improvement” is measured as one of three categories. Thus, it is qualitative.

• The data set is a sample. It contains observations from only 14 of all high school football

players.

1.18 a. The population of interest is all the students in the class. The variable of interest is the GPA of a student in the class.

• Since GPA is measured on a numerical scale, it is quantitative.

• Since the population of interest is all the students in the class and you obtained the GPA

of every member of the class, this set of data would be a census.

• Assuming the class had more than 10 students in it, the set of 10 GPAs would represent

a sample. The set of ten students is only a subset of the entire class.

• This average would have 100% reliability as an "estimate" of the class average, since it

is the average of interest.

• The average GPA of 10 members of the class will not necessarily be the same as the

average GPA of the entire class. The reliability of the estimate will depend on how large the class is and how representative the sample is of the entire population.

• In order for the sample to be a random sample, every member of the class must have an

equal

1.20 a. Flight capability can have only 2 possible outcomes: volant or flightless. Thus, it is qualitative.

• Habitat type can have only 3 possible outcomes: aquatic, ground terrestrial, or aerial

terrestrial. Thus, it is qualitative.

• Nesting site can have only 4 possible outcomes: ground, cavity within ground, tree, or

cavity above ground. Thus, it is qualitative.

• Nest density can have only 2 possible outcomes: high or low. Thus, it is qualitative.

• Diet can have only 4 possible outcomes: fish, vertebrates, vegetables, or invertebrates.

Thus, it is qualitative.

• Body mass is measured in grams, a meaningful number. Thus, it is quantitative.

• Egg length is measured in millimeters, a meaningful number. Thus, it is quantitative.

• Extinct status can have only 3 possible outcomes: extinct, absent from island, or present.

Thus, it is qualitative.

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