Question 1

Identify the type of sampling used.
-A travel industry researcher interviews all of the passengers on five randomly selected cruises. What samplingtechnique is used?

Accepted Answer

This is an example of cluster sampling because the researcher is randomly selecting entire groups (in this case, cruises) and then surveying everyone within those selected groups.

Question 2

Identify the type of sampling used.
-Based on 9000 responses from 26,500 questionnaires sent to all its members, a major medical associationestimated that the annual salary of its members was $99,000 per year. What sampling technique was used?

Accepted Answer

This is an example of simple random sampling because every member of the medical association had an equal chance of being included in the sample when the questionnaires were sent out to all members.

Question 3

Identify the type of sampling used.
-A writer for an art magazine randomly selects and interviews fifty male and fifty female artists. What samplingtechnique is used?

Accepted Answer

The writer uses stratified sampling by dividing the population into two groups (male and female artists) and then randomly selecting individuals from each group to ensure representation of both genders.

Question 4

The city council of a small town needs to determine if the townʹs residents will support the building of a newlibrary. The council decides to conduct a survey of a sample of the townʹs residents. Which one of the followingprocedures would be most appropriate for obtaining a sample of the townʹs residents?

Accepted Answer

Surveying a random sample of persons within each neighborhood of the town ensures that all parts of the town are represented in the sample, making it the most appropriate method for obtaining a representative sample of the town's residents.

Question 5

The top 38 cities in Wisconsin as determined by population are given below. Select a random sample of fourcities from the list below using the two digit list of random numbers provided. Begin with the uppermost leftrandom number and proceed down each column. When a column is complete, use the numbers at the top ofthe next right column and proceed down that column. Information was obtained from the web sitehttp://www.citypopulation.de/USA-Wisconsin.html. \(\begin{array}{l}
\text { Wisconsin Cities by Population }\
\begin{array}{|l|l|l|l|l|l|l|l|l|l|}
\hline 1 & \text { Milwaukee } & 9 & \text { Eau Claire } & 17 & \text { New Berlin } & 25 & \text { West Bend } & 33 & \text { Watertown } \
\hline 2 & \text { Madison } & 10 & \text { Janesville } & 18 & \text { Wausau } & 26 & \text { Superior } & 34 & \text { Muskego } \
\hline 3 & \text { Green Bay } & 11 & \text { West Allis } & 19 & \text { Greenfield } & 27 & \text { Mourt Pleasant } & 35 & \text { De Pere } \
\hline 4 & \text { Kenosha } & 12 & \text { La Crosse } & 20 & \text { Beloit } & 28 & \text { Neenah } & 36 & \text { Fitchburg } \
\hline 5 & \text { Racine } & 13 & \text { Sheboygan } & 21 & \text { Manitowoc } & 29 & \text { Stevens Point } & 37 & \text { South Milwaukee } \
\hline 6 & \text { Appleton } & 14 & \text { Wauwatosa } & 22 & \text { Menomonee Falls } & 30 & \text { Caledonia } & 38 & \text { Grand Chute } \
\hline 7 & \text { Waukesha } & 15 & \text { Fond du Lac } & 23 & \text { Franklin } & 31 & \text { Sun Praine } & & \
\hline 8 & \text { Oshkosh } & 16 & \text { Brookfield } & 24 & \text { Oak Creek } & 32 & \text { Mequon } & & \
\hline
\end{array}
\end{array}\)

$\begin{array}{l}
\text { Random Numbers }\
\begin{array}{|l|l|l|l|l|l|l|l|}
\hline 21 & 49 & 6 & 6 & 19 & 15 & 11 & 17 \
\hline 12 & 43 & 4 & 31 & 7 & 18 & 1 & 43 \
\hline 23 & 30 & 2 & 24 & 21 & 18 & 6 & 48 \
\hline 44 & 12 & 20 & 32 & 2 & 28 & 12 & 38 \
\hline 8 & 30 & 38 & 43 & 41 & 29 & 3 & 13 \
\hline
\end{array}
\end{array}$

Accepted Answer

The random numbers 21, 6, 19, and 15 correspond to the cities Manitowoc, Appleton, Greenfield, and Fond du Lac, respectively.

Question 6

Identify the type of sampling used.
-Thirty-five math majors, 29 music majors and 26 history majors are randomly selected from 585 math majors,279 music majors and 393 history majors at the state university. What sampling technique is used?

Accepted Answer

This is an example of stratified sampling because the population is divided into smaller groups (strata) based on specific characteristics (in this case, their major), and then a random sample is taken from each of these groups.

Question 7

Determine what type of observational study is described. Explain.
-A researcher wanted to determine whether women with children are more likely to develop anxiety disordersthan women without children. She selected a sample of 900 twenty-year old women and followed them for atwenty-year period. At the start of the study, none of the women had children. By the end of the study 53% ofthe women had at least one child. The level of anxiety of each participant was evaluated at the beginning andat the end of the study and the increase (or decrease) in anxiety was recorded. The researchers analyzed theresults to determine whether there was an association between anxiety and having children.

Accepted Answer

This is a cohort study because it involves following a group of individuals over a period of time to see how their exposure to a certain factor (in this case, having children) affects their outcome (in this case, the development of anxiety disorders).

Question 8

Determine what type of observational study is described. Explain.
-Researchers wanted to determine whether there was an association between high blood pressure and thesuppression of emotions. The researchers looked at 1800 adults enrolled in a Health Initiative ObservationalStudy. Each person was interviewed and asked about their response to emotions. In particular they were askedwhether their tendency was to express or to hold in anger and other emotions. The degree of suppression ofemotions was rated on a scale of 1 to 10. Each personʹs blood pressure was also measured. The researchersanalyzed the results to determine whether there was an association between high blood pressure and thesuppression of emotions.

Accepted Answer

This study is cross-sectional because information about both blood pressure and emotional suppression is collected at a single point in time from the participants, rather than over a period of time or from past records.

Question 9

True or False: Experiments assist the researcher in isolating the causes of the relationships that exist betweentwo variables.

Accepted Answer

Experiments allow researchers to manipulate one variable (independent variable) and observe the effect on another variable (dependent variable), thereby helping in isolating and identifying causal relationships between variables.

Question 10

Identify the type of sampling used.
-A statistics student interviews everyone in his apartment building to determine who owns a cell phone. Whatsampling technique is used?

Accepted Answer

The student is using convenience sampling because he is selecting a sample that is easiest to access, namely the people in his apartment building.

Question 11

Determine what type of observational study is described. Explain.
-Vitamin D is important for the metabolism of calcium and exposure to sunshine is an important source ofvitamin D. A researcher wanted to determine whether osteoperosis was associated with a lack of exposure tosunshine. He selected a sample of 250 women with osteoperosis and an equal number of women withoutosteoperosis. The two groups were matched - in other words they were similar in terms of age, diet,occupation, and exercise levels. Histories on exposure to sunshine over the previous twenty years wereobtained for all women. The total number of hours that each woman had been exposed to sunshine in theprevious twenty years was estimated. The amount of exposure to sunshine was compared for the two groups.

Accepted Answer

This is a retrospective study because it involves looking back at past exposure to sunshine to determine its association with osteoporosis.

Question 12

The policy committee at State University has 6 members: LaToyna, Ming, Jose, John, Prof. Rise, andDr. Hernandez. A subcommittee of two members must be formed to investigate the visitation policy in thedormitories. List all possible simple random samples of size 2.

Accepted Answer

Each pair listed in option A represents a unique combination of two members from the committee, accounting for all possible pairs without repetition.

Question 13

The government of a town needs to determine if the cityʹs residents will support the construction of a newtown hall. The government decides to conduct a survey of a sample of the cityʹs residents. Which one of thefollowing procedures would be most appropriate for obtaining a sample of the townʹs residents?

Accepted Answer

Surveying a random sample of persons within each geographic region of the city ensures that all parts of the city are represented, making the sample more likely to accurately reflect the views of the city's entire population.

Question 14

Select a random sample of five state capitals from the list below using the two digit list of random numbersprovided. Begin with the uppermost left random number and proceed down each column. When a column iscomplete, use the numbers at the top of the next right column and proceed down that column.State Capitals \(\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline 1 & \text { Abany, NY } & 11 & \text { Charleston, WV } & 21 & \text { Hartford, CT } & 31 & \text { Madison, WI } & 41 & \text { Richmond, VA } \
\hline 2 & \text { Annapolis, MD } & 12 & \text { Cheyenne, WY } & 22 & \text { Helen, MT } & 32 & \begin{array}{c}
\text { Mortgomery, } \
\text { AL }
\end{array} & 42 & \text { Sacramento, CA } \
\hline 3 & \text { Atlanta, GA } & 13 & \text { Columbia, SC } & 23 & \text { Honolulu, HI } & 33 & \text { Mortpelier, VT } & 43 & \text { Salem, OR } \
\hline 4 & \text { Augusta, ME } & 14 & \text { Columbus, OH } & 24 & \begin{array}{c}
\text { Indianapolis, } \
\text { IN }
\end{array} & 34 & \text { Nashville, TN } & 44 & \begin{array}{c}
\text { Salt Lake City, } \
\text { UT }
\end{array} \
\hline 5 & \text { Austin, TX } & 15 & \text { Concord, NH } & 25 & \text { Jacksor, MS } & 35 & \begin{array}{c}
\text { Oklahoma City, } \
\text { OK }
\end{array} & 45 & \text { Santa Fe, NM } \
\hline 6 & \begin{array}{c}
\text { Baton Rouge, } \
\text { LA }
\end{array} & 16 & \text { Derver, CO } & 26 & \begin{array}{c}
\text { Jefferson } \
\text { City, MO }
\end{array} & 36 & \text { Olymrpia, WA } & 46 & \text { Springfield, IL } \
\hline 7 & \text { Bismarck, ND } & 17 & \text { Des Moines, IA } & 27 & \text { Juneau, AK } & 37 & \text { Phoenix, AZ } & 47 & \text { St. Paul, MN } \
\hline 8 & \text { Boise, ID } & 18 & \text { Dover, DE } & 28 & \text { Lansing, MI } & 38 & \text { Piere, SD } & 48 & \text { Tallahassee, FL } \
\hline 9 & \text { Bostor, MA } & 19 & \text { Frankfort, KY } & 29 & \text { Lincoln, NE } & 39 & \text { Providence, RI } & 49 & \text { Topeka KS } \
\hline 10 & \text { Carson City, NV } & 20 & \text { Hamsbur, PA } & 30 & \begin{array}{c}
\text { Little Rock, } \
\text { AR }
\end{array} & 40 & \text { Raleigh, NC } & 50 & \text { Trenton, NJ } \
\hline
\end{array}\)

$\begin{array}{l}
\text { Random Numbers }\
\begin{array}{|l|l|l|l|l|l|l|l|}
\hline 46 & 81 & 17 & 60 & 92 & 59 & 40 & 9 \
\hline 53 & 78 & 45 & 14 & 53 & 78 & 8 & 43 \
\hline 3 & 99 & 46 & 86 & 41 & 42 & 36 & 95 \
\hline 39 & 14 & 16 & 59 & 84 & 18 & 5 & 48 \
\hline 45 & 41 & 77 & 91 & 11 & 43 & 76 & 28 \
\hline
\end{array}
\end{array}$

Accepted Answer

The correct capitals are selected based on the first five valid random numbers from the list provided that correspond to the numbers assigned to the state capitals. The numbers are 46 (Springfield, IL), 17 (Des Moines, IA), 9 (Boston, MA), 45 (Santa Fe, NM), and 14 (Columbus, OH).

Question 15

Identify the type of sampling used.
-A lobbyist for the oil industry assigns a number to each senator and then uses a computer to randomlygenerate ten numbers. The lobbyist contacts the senators corresponding to these numbers. What samplingtechnique was used?

Accepted Answer

This is an example of simple random sampling because each senator has an equal chance of being selected, and the selection is made randomly without any specific order or grouping.

Question 16

Identify the type of sampling used.
-At a local technical school, five auto repair classes are randomly selected and all of the students from each classare interviewed. What sampling technique is used?

Accepted Answer

This is an example of cluster sampling because entire groups (or clusters) are randomly selected, and then all members of the selected groups are surveyed. In this case, the classes act as clusters.

Question 17

Determine what type of observational study is described. Explain.
-Can money buy happiness? A researcher wanted to determine whether there was any association betweeneconomic status and happiness. She selected a sample of 1000 adults and interviewed them. Each person wasasked about their financial situation and their level of happiness was evaluated. The researcher analyzed theresults to determine whether there was an association between economic status and happiness.

Accepted Answer

This study is a cross-sectional study because information about the participants' economic status and happiness level is collected at a single point in time, rather than over a period of time or by asking participants to recall past events.

Question 18

Determine what type of observational study is described. Explain.
-Researchers wanted to determine whether there was an association between city driving and stomach ulcers.They selected a sample of 900 young adults and followed them for a twenty-year period. At the start of thestudy none of the participants was suffering from a stomach ulcer. Each person kept track of the number ofhours per week they spent driving in city traffic. At the end of the study each participant underwent tests todetermine whether they were suffering from a stomach ulcer. The researchers analyzed the results todetermine whether there was an association between city driving and stomach ulcers.

Accepted Answer

This is a cohort study because individuals (the young adults) were followed over a long period of time (twenty years) to observe the development of a condition (stomach ulcers) in relation to an exposure (city driving).

Question 19

Identify the type of sampling used.
-Every fifth adult entering an airport is checked for extra security screening. What sampling technique is used?

Accepted Answer

Systematic sampling is used when every nth individual is selected from a larger population, in this case, every fifth adult entering an airport.

Question 20

Identify the type of sampling used.
-In a recent online survey, participants were asked to answer ʺyesʺ or ʺnoʺ to the question ʺAre you in favor ofstricter gun control?ʺ 6571 responded ʺyesʺ while 4137 responded ʺnoʺ. There was a fifty-cent charge for thecall. What sampling technique was used?

Accepted Answer

This is an example of convenience sampling because the sample consists of individuals who have self-selected to participate in the survey, likely due to their interest in the topic or willingness to pay the charge, rather than being randomly selected from the population.

Quiz 1: Data Collection

Identify the type of sampling used. -A travel industry researcher interviews all of the passengers on five randomly selected cruises. What samplingtechnique is used?

Identify the type of sampling used. -Based on 9000 responses from 26,500 questionnaires sent to all its members, a major medical associationestimated that the annual salary of its members was $99,000 per year. What sampling technique was used?

Identify the type of sampling used. -A writer for an art magazine randomly selects and interviews fifty male and fifty female artists. What samplingtechnique is used?

Identify the type of sampling used. -Thirty-five math majors, 29 music majors and 26 history majors are randomly selected from 585 math majors,279 music majors and 393 history majors at the state university. What sampling technique is used?

True or False: Experiments assist the researcher in isolating the causes of the relationships that exist betweentwo variables.

Identify the type of sampling used. -A statistics student interviews everyone in his apartment building to determine who owns a cell phone. Whatsampling technique is used?

The policy committee at State University has 6 members: LaToyna, Ming, Jose, John, Prof. Rise, andDr. Hernandez. A subcommittee of two members must be formed to investigate the visitation policy in thedormitories. List all possible simple random samples of size 2.

Identify the type of sampling used. -A lobbyist for the oil industry assigns a number to each senator and then uses a computer to randomlygenerate ten numbers. The lobbyist contacts the senators corresponding to these numbers. What samplingtechnique was used?

Identify the type of sampling used. -At a local technical school, five auto repair classes are randomly selected and all of the students from each classare interviewed. What sampling technique is used?

Identify the type of sampling used. -Every fifth adult entering an airport is checked for extra security screening. What sampling technique is used?