Statistics, Data, and Statistical Thinking

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Chapter 1 Statistics, Data, and Statistical Thinking 1.1 Statistics is a science that deals with the collection, classification, analysis, and interpretation of information or data. It is a meaningful, useful science with a broad, almost limitless scope of applications to business, government, and the physical and social sciences.

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.

1.3 The four elements of a descriptive statistics problem are:

1.The population or sample of interest. This is the collection of all the units upon which the variable is measured.

2.One or more variables that are to be investigated. These are the types of data that are to be collected.

3.Tables, graphs, or numerical summary tools. These are tools used to display the characteristic of the sample or population.

4.Identification of patterns in the data. These are conclusions drawn from what the summary tools revealed about the population or sample.

1.4 The five elements of an inferential statistical analysis are:

1.The population of interest. The population is a set of existing units.

2.One or more variables that are to be investigated. A variable is a characteristic or property of an individual population unit.

3.The sample of population units. A sample is a subset of the units of a population.

4.The inference about the population based on information contained in the sample. A statistical inference is an estimate, prediction, or generalization about a population based on information contained in a sample.

5.A measure of reliability for the inference. The reliability of an inference is how confident one is that the inference is correct.

1.5 The first major method of collecting data is from a published source. These data have already been collected by someone else and are 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 final method of collecting data is observational. 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. The most common type of observational study is a survey.

1.6 Quantitative data are measurements that are recorded on a meaningful numerical scale. Qualitative data are measurements that are not numerical in nature; they can only be classified into one of a group of categories.

1.7 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.Statistics for Business and Economics, 13e (Global Edition) James McClave, George Benson, Terry Sincich (Solutions Manual All Chapters, 100% Original Verified, A+ Grade) 1 / 4

Chapter 1 Copyright © 2019 Pearson Education Ltd.2 1.8 A population is a set of existing units such as people, objects, transactions, or events. A sample is a subset of the units of a population.

1.9 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 An inference without a measure of reliability is nothing more than a guess. A measure of reliability separates statistical inference from fortune telling or guessing. Reliability gives a measure of how confident one is that the inference is correct.

1.11 An example of an unethical statistical practice is when researchers select a biased sample, with the intention of misleading the public.

1.12 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.

1.13 The data consisting of both region names and number codes are qualitative. This is because choosing an arbitrary code (1, 2, etc.) for a name (Africa, Americas, etc.) does not change the type of data.

1.14 Use any of the software packages explained in the section, “Using Technology” on page 31f. Make sure that each of the ten numbers is different since there might be a small chance (≈4.4%) that they are not.

1.15 Both the variables current position and type of organization are qualitative. The variable years of experience is quantitative.

1.16 a.The data would represent the population. These data are all of the data that are of interest to the researchers.b.If the 80 jamming attacks are actually a sample, then the population would be all jamming attacks by the U.S. military over the past several years.c.The variable “network type” is qualitative.d.The variable “number of channels” is qualitative because there are only two categories of possible responses.e.If we wanted to measure the number of channels as a quantitative variable, then we would have to record the exact number of channels for each jamming attack.

1.17 a.The population of interest is the entire set of students that park at the university.b.The sample of interest is the 250 students based on whom data was collected.c.The experimental unit of interest is a single student that parks at the university.d.The variable of interest is the parking time, defined to be the amount of time the student spent finding a parking spot.

1.18 a.High school GPA is a number usually between 0.0 and 4.0. Therefore, it is quantitative.b.Honors/awards would have responses that name things. Therefore, it would be qualitative. 2 / 4

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• 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.

1.19 a. The process of interest is fulfilling customers' orders from receiving the order to it being picked up by the shipping company.

• The variable of interest is whether or not an order has been pulled correctly.

• The sample is the set of all orders that are checked (one every 15 minutes).

• The inference of interest is the number or proportion of all orders that are pulled correctly

(incorrectly).

• Students answers will vary.

1.20 a. The population of interest for this study is the entire set of stocks that are traded on the NYSE.

• The variable being collected is quantitative.

• The data collection method used in this study is: Data from a published source.

• The sample of interest for this study is the 500 NYSE stocks that current prices were collected from.

• The experimental unit of interest for this study is a single stock traded on the NYSE, and the variable

of interest is the current price (or closing price) of an NYSE stock.

1.21 Since the data collected consist of the entire population, this would represent a descriptive study. Flaherty used the data to help describe the condition of the U.S. Treasury in 1861.

1.22 a. The population of interest is the status of computer crime at all United States businesses and government agencies.

• The method of data collection was a survey. Since not all of those who were sent a survey

responded, the sample was self-selected. The results are probably not representative of the population. Usually, those who respond to surveys have very strong opinions, either positive or negative.

• The variable of interest is whether or not the firm or agency had unauthorized use of its computer

systems during the year. Since the response would be either yes or no, the variable would be qualitative.

• If the sample was representative, we could infer that approximately 41% of all U. S. corporations and

government agencies experienced unauthorized use of their computer systems during the year.

1.23 a. This is a designed experiment because the college students were randomly assigned to a group.

• The experimental unit is a college student.
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• The two variables are type of condition and type of disposal. Both type of condition and type of

disposal are qualitative.

• We could infer that in the population of all college students, those who could be placed in the

usefulness is salient condition will recycle at a much higher rate (68%) than those who could be placed in the control condition (37%).

1.24 a. The experimental unit of interest is a college student.

• Both the variables street crossing performance score and memory task score are quantitative

variables.

• This is an application of inferential statistics. Data were collected from a sample of students and

conclusions were made about the entire population based on the information found in the sample.

1.25 a. The experimental unit for this study is a single-family residential property in Arlington, Texas.

• The variables measured are the sale price and the Zillow estimated value. Both of these variables are

quantitative.

• If these 2,045 properties were all the single-family residential properties sold in Arlington, Texas in

the past 6 months, then this would be considered the population.

• If these 2,045 properties represent a sample, then the population would be all the singe-family

residential properties sold in the last 6 months in Arlington, Texas.

• No. The real estate market across the United States varies greatly. The prices of single-family

residential properties in this small area are probably not representative of all properties across the United States.

1.26 a. The experimental unit for this study is an NFL quarterback.

• The variables measured in this study include draft position, NFL winning ratio, and QB production

score. Since the draft position was put into 3 categories, it is a qualitative variable. The NFL winning ratio and the QB production score are both quantitative.

• Since we want to project the performance of future NFL QBs , this would be an application of

inferential statistics.

1.27 a. The population of interest is all individuals who took GMAT in the time period.

• The method of data collection was a survey.
• This is probably not a representative sample. The sample was self-selected. Not all of those who

were selected for the study responded to all four surveys. Those who did respond to all 4 surveys probably have very strong opinions, either positive or negative, which may not be representative of all of those in the population.

1.28 a. The population of interest is all CPA firms.

• A survey was used to collect the data.
• This sample was probably not representative. Not all of those selected to be in the sample responded.

In fact, only 992 of the 23,500 people who were sent the survey responded. Generally, those who do

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