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Chapter 1: Q4E (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

Exercise 34 presented the following data on endotoxin concentration in settled dust both for a sample of urban homes and for a sample of farm homes:

U: 6.0 5.0 11.0 33.0 4.0 5.0 80.0 18.0 35.0 17.0 23.0

F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.0

9.2 3.0 2.0 0.3

a. Determine the value of the sample standard deviation for each sample, interpret these values, and then contrast variability in the two samples. (Hint:\(\sum {{x_i}} \)= 237.0 for the urban sample and =128.4 for the farm sample, and\(\sum {x_i^2} \)= 10,079 for the urban sample and 1617.94 for the farm sample.)

b. Compute the fourth spread for each sample and compare. Do the fourth spreads convey the same message about variability that the standard deviations do? Explain.

c. Construct a comparative boxplot (as did the cited paper)and compare and contrast the four samples.

The amount of flow through a solenoid valve in an automobile鈥檚

pollution-control system is an important characteristic. An experiment was carried out to study how flow rate depended on three factors: armature length, spring load, and bobbin depth. Two different levels (low and high) of each factor were chosen, and a single observation on flow was made for each combination oflevels.

a. The resulting data set consisted of how manyobservations?

b. Is this an enumerative or analytic study? Explainyour reasoning.

An experiment to study the lifetime (in hours) for acertain type of component involved putting ten components into operation and observing them for 100hours. Eight of the components failed during that

period, and those lifetimes were recorded. Denote the lifetimes of the two components still functioning after100 hours by 100+. The resulting sample observations were

48 79 100+ 35 92 86 57 100+ 17 29

Which of the measures of center discussed in this section can be calculated, and what are the values of those measures? (Note:The data from this experiment is said to be 鈥渃ensored on the right.鈥�)

Allowable mechanical properties for structural design of metallic aerospace vehicles requires an approved method for statistically analyzing empirical test data. The article 鈥淓stablishing Mechanical Property Allowables for Metals鈥� (J. of Testing and Evaluation, 1998: 293鈥�299) used the accompanying data on tensile ultimate strength (ksi) as a basis for addressing the difficulties in developing such a method.

122.2 124.2 124.3 125.6 126.3 126.5 126.5 127.2 127.3

127.5 127.9 128.6 128.8 129.0 129.2 129.4 129.6 130.2

130.4 130.8 131.3 131.4 131.4 131.5 131.6 131.6 131.8

131.8 132.3 132.4 132.4 132.5 132.5 132.5 132.5 132.6

132.7 132.9 133.0 133.1 133.1 133.1 133.1 133.2 133.2

133.2 133.3 133.3 133.5 133.5 133.5 133.8 133.9 134.0

134.0 134.0 134.0 134.1 134.2 134.3 134.4 134.4 134.6

134.7 134.7 134.7 134.8 134.8 134.8 134.9 134.9 135.2

135.2 135.2 135.3 135.3 135.4 135.5 135.5 135.6 135.6

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137.8 137.8 137.8 137.9 137.9 138.2 138.2 138.3 138.3

138.4 138.4 138.4 138.5 138.5 138.6 138.7 138.7 139.0

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a. Construct a stem-and-leaf display of the data by first deleting (truncating) the tenths digit and then repeating each stem value five times (once for leaves 1 and 2, a second time for leaves 3 and 4, etc.). Why is it relatively easy to identify a representative strength value?

b. Construct a histogram using equal-width classes with the first class having a lower limit of 122 and an upper limit of 124. Then comment on any interesting features of the histogram.

The National Health and Nutrition Examination Survey (NHANES) collects demographic, socioeconomic, dietary, and health related information on an annual basis. Here is a sample of \({\rm{20}}\) observations on HDL cholesterol level \({\rm{(mg/dl)}}\) obtained from the \({\rm{2009 - 2010}}\) survey (HDL is 鈥済ood鈥� cholesterol; the higher its value, the lower the risk for heart disease):

\(\begin{array}{l}{\rm{35 49 52 54 65 51 51}}\\{\rm{47 86 36 46 33 39 45}}\\{\rm{39 63 95 35 30 48}}\end{array}\)

a. Calculate a point estimate of the population mean HDL cholesterol level.

b. Making no assumptions about the shape of the population distribution, calculate a point estimate of the value that separates the largest \({\rm{50\% }}\) of HDL levels from the smallest \({\rm{50\% }}\).

c. Calculate a point estimate of the population standard deviation.

d. An HDL level of at least \({\rm{60}}\) is considered desirable as it corresponds to a significantly lower risk of heart disease. Making no assumptions about the shape of the population distribution, estimate the proportion \({\rm{p}}\) of the population having an HDL level of at least \({\rm{60}}\).
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