Part IV: Complete Solutions, Chapter 1
3
Chapter 1: Getting Started
Section 1.1
1.
Individuals are people or objects included in the study, whereas a variable is a characteristic of the individual
that is measured or observed.
2.
Nominal data are always qualitative.
3.
A parameter is a numerical measure that describes a population. A statistic is a numerical value that describes a
sample.
4.
If the population does not change, a parameter will not change. Thus, for a fixed population, parameter values
are constant. Surely, if we take three samples of the same size from a population, the values of the sample
statistics will differ.
5.
(a) The variable is the response regarding frequency of eating at fast-food restaurants.
(b) The variable is qualitative. The categories are the number of times one eats in fast-food restaurants.
(c) The implied population is responses for all adults in the United States.
6.
(a) The variable is miles per gallon.
(b) The variable is quantitative because arithmetic operations can be applied to the mpg values.
(c) The implied population is gasoline mileage for all new cars.
7.
(a) The variable is the nitrogen concentration (milligrams of nitrogen/liter of water).
(b) The variable is quantitative because arithmetic operations can be applied to nitrogen concentration.
(c) The implied population is all the lakes in the wetlands.
8.
(a) The variable is the number of ferromagnetic artifacts per 100 square meters.
(b) The variable is quantitative because arithmetic operations can be applied to the number of artifacts.
(c) The implied population is the number of ferromagnetic artifacts per each distinct 100-square-meter plot in
the Tara region.
9.
(a) Length of time to complete an exam is a ratio level of measurement. The data may be arranged in order,
differences and ratios are meaningful, and a time of 0 is the starting point for all measurements.
(b) Time of first class is an interval level of measurement. The data may be arranged in order, and differences
are meaningful.
(c) Major field of study is a nominal level of measurement. The data consist of names only.
(d) Course evaluation scale is an ordinal level of measurement. The data may be arranged in order.
(e) Score on last exam is a ratio level of measurement. The data may be arranged in order, differences and
ratios are meaningful, and a score of 0 is the starting point for all measurements.
(f) Age of student is a ratio level of measurement. The data may be arranged in order, differences and ratios are
meaningful, and an age of 0 is the starting point for all measurements.
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Part IV: Complete Solutions, Chapter 1
4
10. (a) Salesperson’s performance is an ordinal level of measurement. The data may be arranged in order.
(b) Price of company’s stock is a ratio level of measurement. The data may be arranged in order, differences
and ratios are meaningful, and a price of 0 is the starting point for all measurements.
(c) Names of new products is a nominal level of measurement. The data consist of names only.
(d) Room temperature is an interval level of measurement. The data may be arranged in order, and differences
are meaningful.
(e) Gross income is a ratio level of measurement. The data may be arranged in order, differences and ratios are
meaningful, and an income of 0 is the starting point for all measurements.
(f) Color of packaging is a nominal level of measurement. The data consist of names only.
11. (a) Species of fish is a nominal level of measurement. Data consist of names only.
(b) Cost of rod and reel is a ratio level of measurement. The data may be arranged in order, differences and
ratios are meaningful, and a cost of 0 is the starting point for all measurements.
(c) Time of return home is an interval level of measurement. The data may be arranged in order, and
differences are meaningful.
(d) Guidebook rating is an ordinal level of measurement. Data may be arranged in order.
(e) Number of fish caught is a ratio level of measurement. The data may be arranged in order, differences and
ratios are meaningful, and 0 fish caught is the starting point for all measurements.
(f) Temperature of the water is an interval level of measurement. The data may be arranged in order, and
differences are meaningful.
12. Form B would be better. Statistical methods can be applied to the ordinal data obtained from Form B but not to
the answers obtained from Form A.
13. (a) Answers vary. Ideally, weigh the packs in pounds using a digital scale that has tenths of pounds for
accuracy.
(b) Some students may refuse to allow the weighing.
(c) Informing students before class may cause students to remove items before class.
Section 1.2
1.
In stratified samples, we select a random sample from each stratum. In cluster sampling, we randomly select
clusters to be included, and then each member of the selected cluster is sampled.
2.
In simple random samples, every sample of size n has an equal chance of being selected. In a systematic
sample, the only possible samples are those including every kth member of the population with respect to the
random starting position.
3.
Sampling error is the difference between the value of the population parameter and the value of the sample
statistic that stems from the random selection process. Certainly, larger boxes of cereal will cost more than
small boxes of cereal.
4.
(a) Yes, your seating location and the randomized coin flip ensure equal chances of being selected.
(b) Not using the described method of selection. This is not a simple random sample; it is a cluster sample.
(c) Simply assign each student a number 1, 2, . . . , 40 and use a computer or a random-number table to select
20 students.
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Part IV: Complete Solutions, Chapter 1
5.
Simply use a computer or random-number table to randomly selected n students from the class after numbers
are assigned.
(a) Answers vary. Perhaps they are excellent students who make a special effort to get to class early.
(b) Answers vary. Perhaps they are busy students who are never on time to class.
(c) Answers vary. Perhaps students in the back row are introverted.
(d) Answers vary. Perhaps tall students generally are healthier.
6.
(a) Sick students and those who are skipping class cannot be sampled.
(b) Home-schooled students, homeless students, and dropouts cannot be sampled.
7.
Answers vary.
8.
Answers vary.
9.
Answers vary.
5
10. Answers vary. Perhaps use 0, 1, 2, 3, 4 to indicate H and 5, 6, 7, 8, 9 to indicate T.
11. (a) It is appropriate. Certainly we can roll a 1 more than once in 20 rolls. The fourth roll was 2.
(b) No, simulated rolls of the die are random events, and we certainly would expect a different sequence.
12. Answers vary. We do expect at least once match on birthdays on over 50% of the times we run this experiment.
13. Answers vary.
14. Answers vary.
15. (a) This technique is simple random sampling. Every sample of size n from the population has an equal chance
of being selected, and every member of the population has an equal chance of being included in the sample.
(b) This technique is cluster sampling. The state, Hawaii, is divided into ZIP Codes. Then, within each of the
10 selected ZIP Codes, all businesses are surveyed.
(c) This technique is convenience sampling. This technique uses results or data that are conveniently and
readily obtained.
(d) This technique is systematic sampling. Every fiftieth business is included in the sample.
(e) This technique is stratified sampling. The population was divided into strata based on business type. Then a
simple random sample was drawn from each stratum.
16. (a) This technique is stratified sampling. The population was divided into strata (four categories of length of
hospital stay), and then a simple random sample was drawn from each stratum.
(b) This technique is simple random sampling.
(c) This technique is cluster sampling. There are five geographic regions, and some facilities from each region
are selected randomly. Then, for each selected facility, all patients on the discharge list are surveyed to
create the patient satisfaction profiles.
(d) This technique is systematic sampling. Every 500th patient is included in the sample.
(e) This technique is convenience sampling. This technique uses results or data that are conveniently and
readily obtained.
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Part IV: Complete Solutions, Chapter 1
6
Section 1.3
1.
Answers vary. People with higher incomes likely will have high-speed Internet access, which will lead to
spending more time on-line. Spending more time on-line might lead to spending less time watching TV. Thus,
spending less time watching TV cannot be attributed solely to high income or high-speed Internet access.
2.
A double-blind procedure would entail neither the patients nor those administering the treatments knowing
which patients received which treatments. This process should eliminate potential bias from the treatment
administrators and from patient psychology regarding benefits of the drug.
3.
(a) This is an observational study because observations and measurements of individuals are conducted in a
way that doesn’t influence the response variable being measured.
(b) This is an experiment because a treatment is deliberately imposed on the bighorn sheep in order to observe
a possible change in heartworm prevention.
(c) This is an experiment because a treatment is deliberately imposed on the fishermen in order to observe a
possible change in the length of fish in the river.
(d) This is an observational study because observations of the turtles are conducted in a way that doesn’t
change the response being measured.
4.
(a)
(b)
(c)
(d)
5.
(a) Use random selection to pick 10 calves to inoculate. After inoculation, test all calves to see if there is a
difference in resistance to infection between the two groups. No placebo is being used.
(b) Use random selection to pick nine schools to visit. After the police visits, survey all the schools to see if
there is a difference in views between the two groups. No placebo is being used.
(c) Use random selection to pick 40 volunteers for the skin patch with the drug. Then record the smoking
habits of all volunteers to see if a difference exists between the two groups. A placebo patch is used for the
remaining 35 volunteers in the second group.
6.
(a) “Over the last few years” could mean 2 years, 3 years, 7 years, etc. A more precise phrase is “Over the past
5 years.”
(b) If a respondent is first asked, “Have you ever run a stop sign,” chances are that their response to the
question, “Should fines be doubled,” will change. Those who run stop signs probably don’t want the fine to
double.
(c) When only yes or no are possible, most people likely will choose no. When, rarely, sometimes, and
frequently are possible, most people likely will choose rarely or sometimes.
7.
Based on the information, Scheme A will be better because the blocks are similar. The plots bordering the river
should be similar, and the plots away from the river should be similar.
Sampling was used in the hospitals.
A computer simulation was used to mimic flight.
A census was used because all data were used by the NFL.
This was an experiment; patients were assigned a treatment, and the change in precancerous lesions was
measured.
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Part IV: Complete Solutions, Chapter 1
7
Chapter 1 Review
1.
(a) Stratified
(b) All undergraduates at the specific campus studied
(c) The variable is number of hours worked. It is quantitative. It is a ratio.
(d) The variable is career applicability. It is qualitative. It is ordinal.
(e) It is a statistic.
(f) The nonresponse rate is 60%, and it most likely will introduce bias into the study because those who do not
answer may have different experiences than those who do answer.
(g) Probably not. These results are most applicable only to the campus in the study.
2.
The implied population is all the listeners (or even all the voters). The variable is the voting preference of a
caller. There is probably bias in the selection of the sample because those with the strongest opinions are most
likely to call in.
3.
Using the random-number table, pick seven digits at random. Digits 0, 1, and 2 can correspond to “Yes,” and
digits 3, 4, 5, 6, 7, 8, and 9 can correspond to “No.” This will effectively simulate a random draw from a
population with 30% TIVO owners.
4.
(a)
(b)
(c)
(d)
(e)
5.
(a) This is an observational study because no treatments were applied.
(b) This is an experiment because a treatment was applied (test type) and the results then were compared.
6.
(a) Randomly select 500 donors to receive the literature and 500 donors to receive the phone call. After the
donation collection period, compare the average amount or total amount collected from each of the two
treatment groups.
(b) Randomly select the 43 adults to be given the treatment gel and the 42 adults to receive the placebo gel.
After the treatment period, compare the whiteness of the two groups. To make this double blind, neither the
treatment administrators nor would the patients would know which gel the patients are receiving.
7.
Questions should be worded in a clear, concise, and unbiased manner. No questions should be misleading.
Commonsense rules should be stated for any numerical answers.
8.
No response required.
9.
(a) This is an experiment; the treatment was the amount of light given to the colonies.
(b) We can assume that the normal-light group is the control group because this simulates normal light patterns
for the fireflies. Therefore, the constant-light group is the treatment group.
(c) Number of fireflies alive at the end of the study
(d) Ratio
Cluster
Convenience
Systematic
Simple random
Stratified
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