SOLUTIONS MANUAL - Chapter 2 Measurement in Statistics ..............

SOLUTIONS MANUAL

STATISTICAL

REASONING

FOR EVERYDAY

LIFE

FIFTH EDITION

Jeffrey Bennett William L. Briggs Mario F. Triola 1 / 4

iii Contents Chapter 1 Speaking of Statistics .................................................................................................................. 1 Chapter 2 Measurement in Statistics ......................................................................................................... 9 Chapter 3 Visual Displays of Data .......................................................................................................... 17 Chapter 4 Describing Data .......................................................................................................................... 27 Chapter 5 A Normal World ......................................................................................................................... 37 Chapter 6 Probability in Statistics ........................................................................................................... 45 Chapter 7 Correlation and Causality ...................................................................................................... 53 Chapter 8 Inferences from Samples to Populations ........................................................................ 61 Chapter 9 Hypothesis Testing .................................................................................................................... 67 Chapter 10 t Tests, Two-Way Tables, and ANOVA ...................................................................... 73 2 / 4

Copyright © 2018 Pearson Education, Inc. 1

CHAPTER 1

Section 1.1 Statistical Literacy and Critical Thinking

1 The two meanings are: (1) statistics is the science of collecting,

organizing, and interpreting data; and (2) statistics are the data (numbers or other pieces of information) that describe or summarize some characteristic from a sample. Note that for the first meaning, the word “statistics” is singular and for the second it is plural.

• A population is the complete set of people or things being studied, while a

sample is a subset of a population. In other words, the sample is only a part of the complete population. A population parameter is a characteristic of a population. A sample statistic is a characteristic of a sample found by consolidating or summarizing raw data. Raw data are all measurements or observations collected. It is usually impractical to directly measure population parameters for large populations, so we usually infer likely values of the population parameters from the measured sample statistics.

• The margin of error is used to describe the range of values in a confidence

interval. We add and subtract the margin of error from a sample statistic to find the confidence interval, or the range of values that is likely to contain some population parameter. The confidence interval is used to estimate the population parameter, and the confidence level (e.g. 95%) tells us how confident we should be that the population parameter lies within the quoted range.

4 The basic steps, summarized in Figure 1.1, are: (1) identify the goals; (2)

choose a representative sample from the population; (3) collect raw data from the sample and summarize them with sample statistics; (4) use the sample statistics to make inferences about the population; (5) draw conclusions from your results. Students should come up with their own example.

• This statement does not make sense. The statement is drawing a conclusion

about all American adults, which means it is identifying the exact value of a population parameter. But the pollster only surveyed a sample of 1009 adults, so it is not possible to know with certainty the value of the population parameter.

• This statement does make sense. The margin of error suggests a (presumably

95%) confidence interval from 52% to 58%. However, there is always some chance that the actual population proportion is outside the confidence interval, and in this case it would not need to be far outside for the candidate to lose. Moreover, the poll was taken 2 months before the election, and voters may change their minds by election time.

• This statement does not make sense. A margin of error of zero would imply

that there is no uncertainty in a survey result, and that could happen only if the entire population was surveyed, rather than just a sample.

• This statement does not make sense. The confidence interval tells us that

we can have 95% confidence that the values from 55% to 60% contain the population parameter, but we cannot be absolutely certain that the true population parameter isn’t significantly lower or higher.

• This statement does not make sense. Inferences about one population (males)

do not necessarily apply to a different population (females).10 This statement does make sense. The purpose of statistics is to help with decision making, and if the survey was conducted well, it is possible to draw conclusions with high confidence from a survey of a 1000-person sample.If the survey results indicate that most people like the song, then it makes sense to promote it, even though there is no guarantee that the promotion will be successful. 3 / 4

2 CHAPTER 1, SPEAKING OF STATISTICS

Copyright © 2018 Pearson Education, Inc.

Concepts and Applications

11 Sample: the 1018 adults selected. Population: the complete set of all

adults (presumably in the United States). Sample statistic: 22%. The

value of the population parameter is not known, but it is the percentage of all adults (presumably in the United States) who smoked cigarettes in the past week.12 Sample: the 186 babies selected. Population: the complete set of all

babies. Sample statistic: 3103 g. The value of the population

parameter is not known, but it is the average (mean) birth weight of all babies.13 Sample: the 47 subjects treated with Garlicin. Population: the

complete set of all adults. Sample statistic: 3.2 mg/dL. The value of

the population parameter is not known, but it is the average (mean) change in LDL cholesterol.14 Sample: the 150 senior executives who were surveyed. Population: the

complete set of all senior executives. Sample statistic: 47%. The

value of the population parameter is not known, but it is the percentage of all senior executives who say that the most common job interview mistake is to have little or no knowledge of the company where the applicant is being interviewed.15 The range of values likely to contain the true value of the population parameter is from 77% - 2% to 77% + 2% or from 75% to 79%.16 The range of values likely to contain the true value of the population parameter is from 85% - 1% to 85% + 1% or from 84% to 86%.17 The range of values likely to contain the true value of the population parameter is from 96% – 3% to 96% + 3% or from 93% to 99%.18 The range of values likely to contain the true value of the population parameter (mean body temperature) is 98.2º F – 0.1º F to 98.2º F + 0.1º F or from 98.1º F to 98.3º F degrees.19 The range of values likely to contain the true value of the population parameter is from 57% – 4% to 57% + 4% or from 53% to 61%.20 The range of values likely to contain the true value of the population parameter is from 0.032% – 0.006% to 0.032% + 0.006% or from 0.026% to

0.038%.

21 Based on the survey, the actual percentage of voters is expected to be between 67% and 73%, which does not include the 61% value from actual voting records. If the survey was conducted well, then it is unlikely that its result would be so different from the actual voter turnout, implying either that respondents intentionally lied to appear favorable to the pollsters or that their memories may have been faulty.22 It appears that the men who were surveyed may have been influenced by the gender of the interviewer. When they were interviewed by women, they may have been more inclined to respond in a way that they thought was more favorable to the female interviewers.23 Yes, we can safely conclude that fewer than half of all students say they are tired on most days. Based on the confidence interval and margin of error, it is likely that the actual population parameter is fairly close to the 39% sample statistic, and very unlikely that the true value could be above 50%.24 No, the results do not contradict Mendel’s theory. Using the margin of error, it appears that the percentage of yellow peas is likely to be between 22% and 30%, and that range of values includes Mendel’s claimed value of 25%, so the results do not contradict his theory.

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