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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

The weekly demand for propane gas (in \({\rm{1000s}}\) of gallons) from a particular facility is an \({\rm{rv}}\) \({\rm{X}}\) with pdf

\({\rm{f(x) = }}\left\{ {\begin{array}{*{20}{c}}{{\rm{2}}\left( {{\rm{1 - }}\frac{{\rm{1}}}{{{{\rm{x}}^{\rm{2}}}}}} \right)}&{{\rm{1}} \le {\rm{x}} \le {\rm{2}}}\\{\rm{0}}&{{\rm{ otherwise }}}\end{array}} \right.\)

a. Compute the cdf of \({\rm{X}}\).

b. Obtain an expression for the \({\rm{(100p)th}}\) percentile. What is the value of \({\rm{\tilde \mu }}\)?

c. Compute \({\rm{E(X)}}\) and \({\rm{V(X)}}\).

d. If \({\rm{1}}{\rm{.5}}\) thousand gallons are in stock at the beginning of the week and no new supply is due in during the week, how much of the \({\rm{1}}{\rm{.5}}\) thousand gallons is expected to be left at the end of the week? (Hint: Let \({\rm{h(x) = }}\) amount left when demand \({\rm{ = x}}\).)

A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of the article 鈥淓ffects of Short Term Supplementation with Selenised Yeast on Milk Production and Composition of Lactating Cows鈥� (Australian J. of Dairy Tech., 2004: 199鈥�203) supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement and a control sample given no supplement, both initially and after a 9-day period.

Obs

InitSe

InitCont

FinalSe

FinalCont

1

11.4

9.1

138.3

9.3

2

9.6

8.7

104.0

8.8

3

10.1

9.7

96.4

8.8

4

8.5

10.8

89.0

10.1

5

10.3

10.9

88.0

9.6

6

10.6

10.6

103.8

8.6

7

11.8

10.1

147.3

10.4

8

9.8

12.3

97.1

12.4

9

10.9

8.8

172.6

9.3

10

10.3

10.4

146.3

9.5

11

10.2

10.9

99.0

8.4

12

11.4

10.4

122.3

8.7

13

9.2

11.6

103.0

12.5

14

10.6

10.9

117.8

9.1

15

10.8

121.5

16

8.2

93.0

a. Do the initial Se concentrations for the supplementand control samples appear to be similar? Use various techniques from this chapter to summarize thedata and answer the question posed.
b. Again use methods from this chapter to summarizethe data and then describe how the final Se concentration values in the treatment group differ fromthose in the control group.

A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape (鈥淥xygen Consumption and Ventilation During Escape from an Offshore Platform,鈥� Ergonomics, 1997: 281鈥�292):

389 356 359 363 375 424 325 394 402

373 373 370 364 366 364 325 339 393

392 369 374 359 356 403 334 397

a. Construct a stem-and-leaf display of the data. How does it suggest that the sample mean and median will compare?

b. Calculate the values of the sample mean and median.(Hint:\(\sum {{x_i} = } \)9638.)

c. By how much could the largest time, currently 424, be increased without affecting the value of the sample median? By how much could this value be decreased without affecting the value of the sample median?

d. What are the values of \(\bar x\)and \(\tilde x\), when the observations are re expressed in minutes?

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.

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The article 鈥淓ffects of Short-Term Warming on Low and High Latitude Forest Ant Communities鈥� (Ecoshpere, May 2011, Article 62) described an experiment in which observations on various characteristics were made using mini chambers of three different types: (1) cooler (PVC

frames covered with shade cloth), (2) control (PVC frames only), and (3) warmer (PVC frames covered with plastic).One of the article鈥檚 authors kindly supplied the accompanying data on the difference between air and soil temperatures(掳C).

Cooler Control Warmer

1.59 1.92 2.57

1.43 2.00 2.60

1.88 2.19 1.93

1.26 1.12 1.58

1.91 1.78 2.30

1.86 1.84 0.84

1.90 2.45 2.65

1.57 2.03 0.12

1.79 1.52 2.74

1.72 0.53 2.53

2.41 1.90 2.13

2.34 2.86

0.83 2.31

1.34 1.91

1.76

a. Compare measures of center for the three different samples.

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