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Chapter 1: 1.1 (page 12)

a. Give three different examples of concrete populations and three different examples of hypothetical populations.

b. For one each of your concrete and your hypothetical populations, give an example of a probability question and an example of an inferential statistics question.

Short Answer

Expert verified

a.

Examples of concrete populations include all workers at a company, all students who take the NEET exam in the year 2021 etc.

The examples of hypothetical populations are the Page length of the research paper published in 2012, Average students participating in a scholarship exam at a university in the next academic year etc.

b.

An example of probability questions from a concrete population is, what is the probability of getting at most one king?

An example of probability questions from a hypothetical population is, what is the probability of medicine being more toxic than 15 units?

Step by step solution

01

Providing example from concrete populations

A concrete population is a well-defined and measurable population.

The examples of concrete populations are:

1. All workers at a company.

2. The number of students participating in a maths Olympiad.

3. All students who take the NEET exam in the year 2021.

02

Providing example from hypothetical populations

The population consists of all possible strength measurements that might be made under similar experimental conditions.

The examples of hypothetical populations are,

1. Page length of the research paper published in 2012.

2. The possible samples from a particular type of cancer tissue.

3. Average students participated in a scholarship exam at a university in the next academic year.

03

Providing examples of probability questions from concrete populations

The examples of probability questions are as follows,

1. What is the probability of getting at most 1 king?

2. What is the probability of getting a king?

3. What is the probability of getting 3 heads when three coins are tossed once?

04

Providing examples of probability questions from hypothetical populations

The examples of probability questions are as follows,

1. What is the probability of medicine being more toxic than 15 units?

2. What is the probability of throwing a ball more than 200 meters?

3. What is the probability of an average student scoring more than a grade of 4.9?

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Most popular questions from this chapter

A certain city divides naturally into ten district neighborhoods.How might a real estate appraiser select a sample of single-family homes that could be used as a basis for developing an equation to predict appraised value from characteristics such as age, size, number of bathrooms, distance to the nearest school, and so on? Is the study enumerative or analytic?

Give one possible sample of size 4 from each of the following

populations:

a. All daily newspapers published in the United States

b. All companies listed on the New York Stock Exchange

c. All students at your college or university

d. All grade point averages of students at your college or university

The accompanying frequency distribution of fracture strength (MPa) observations for ceramic bars fired in aparticular kiln appeared in the article “Evaluating TunnelKiln Performance” (Amer. Ceramic Soc. Bull., Aug.1997: 59–63).

Class81-<83 83-<85 85-<87 87-<89 89-<91

Frequency6 7 17 30 43

Class91-<93 93-<95 95-<97 97-<99

Frequency28 22 13 3

  1. Construct a histogram based on relative frequencies, and comment on any interesting features.
  2. What proportion of the strength observations are at least 85? Less than 95?

c. Roughly what proportion of the observations are less than 90?

A transformation of data values by means of some mathematical function, such as\(\sqrt x \)or\(1/x\), can often yield a set of numbers that has “nicer” statistical properties than the original data. In particular, it may be possible to find a function for which the histogram of transformed values is more symmetric (or, even better, more like a bell-shaped curve) than the original data. As an example, the article “Time Lapse Cinematographic Analysis of Beryllium–Lung FibroblastInteractions” (Environ. Research,1983: 34–43) reported the results of experiments designed to study the behavior of certain individual cells that had been exposed to beryllium. An important characteristic of such an individual cell is its interdivision time (IDT). IDTs were determined for a large number of cells, both in exposed (treatment) and unexposed(control) conditions. The authors of the articleused a logarithmic transformation, that is, transformed value=log(original value). Consider the following representative IDT data:

IDT log10(IDT) IDT log10(IDT) IDT log10(IDT)

28.1 1.45 60.1 1.78 21.0 1.32

31.2 1.49 23.7 1.37 22.3 1.35

13.7 1.14 18.6 1.27 15.5 1.19

46.0 1.66 21.4 1.33 36.3 1.56

25.8 1.41 26.6 1.42 19.1 1.28

16.8 1.23 26.2 1.42 38.4 1.58

34.8 1.54 32.0 1.51 72.8 1.86

62.3 1.79 43.5 1.64 48.9 1.69

28.0 1.45 17.4 1.24 21.4 1.33

17.9 1.25 38.8 1.59 20.7 1.32

19.5 1.29 30.6 1.49 57.3 1.76

21.1 1.32 55.6 1.75 40.9 1.61

31.9 1.50 25.5 1.41

28.9 1.46 52.1 1.72

Use class intervals 10-<20, 20-<30,… to construct a histogram of the original data. Use intervals1.1-<1.2, 1.2-<1.3,… to do the same for the transformed data. What is the effect of the transformation?

A Pareto diagram is a variation of a histogram forcategorical data resulting from a quality control study.Each category represents a different type of product non-conformity or production problem. The categories areordered so that the one with the largest frequencyappears on the far left, then the category with the secondlargest frequency, and so on. Suppose the following information on nonconformities in circuit packs isobtained: failed component, 126; incorrect component,210; insufficient solder, 67; excess solder, 54; missingcomponent, 131. Construct a Pareto diagram.
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