# MATH225 Week 1 Assignment Sampling Methods (July 2019)

MATH 225 Statistical Reasoning for the Health Sciences

Week 1 Assignment Sampling Methods

Question Raymond wants to estimate the percentage of parents who use cloth diapers. He asks a randomly selected group of 200 parents whether or not they use cloth diapers. What is the data?

the percentage of all parents who use cloth diapers

the 200 people surveyed

all parents who use cloth diapers

the percentage of surveyed parents who use cloth diapers

specific “yes” or “no” responses to the survey

Question Is the statement below true or false?

A sample is all individuals, objects, or measurements whose properties are being studied.

True

False

Question There are 6000 people who attended a political debate at a convention center. There are three candidates who are participating in the debate – Mr. Smith, Mr. Jones, or Ms. Roberts. You want to find out which candidate is most popular amongst the people attending. You ask 500 people as they walk into the convention center.

Which represents the population in this scenario?

The three candidates – Mr. Smith, Mr. Jones, and Ms. Roberts

The 500 people surveyed

The 6000 people attending the debate

Everyone who has been the convention center that month

Question You want to find the average test score of the students in every math class in 11th grade. There are 15math classes in 11th grade. You survey the scores of 7 math classes, and you calculate that the average test score is 83%.

Which of the following represent the sample and the parameter in this scenario?

Sample: 7 math classes

Parameter: There is no parameter in this scenario.

Sample: 7 math classes

Parameter: the average test score of 83%

Sample: 15 math classes

Parameter: There is no parameter in this scenario.

Sample: 15 math classes

Parameter: the average test score of 83%

Statistics and Data

The science of statistics deals with the collection, analysis, interpretation, and presentation of data. We see and use data in our everyday lives.

In statistics, we generally want to study a population. A population is a total collection of persons, things, or objects under study. Gathering information about an entire population often costs too much or is virtually impossible. Instead, we collect a sample of the population or a smaller portion of the larger population. This is usually easier to do, and gives us a good idea of what’s going on in the population. A sample should have the same characteristics as the population it is representing.

Data are information about populations or samples. Generally, there are unknown characteristics, or variables, about a population that we wish to know. To obtain this information, we collect data by sampling some members of a population. Once collected, the data are used as the actual values of the variables. Data may be numbers (quantitative data) or they may be words (qualitative data).

Example 1You want to determine the overall grade point average (GPA) at your school. There are 1800 students at your school. Since you want to collect data about all of the students, all 1800 students is the population. The variable is overall GPA at your school.

But, it would be difficult to ask every single one of the 1800 students in your school about his/her GPA. So, it would make sense to gain information from a smaller group of students who attend your school. So, you survey 200 random students. This portion of the population is called the sample.

The grade point averages of the students surveyed would be the data collected.

A statistic and a parameter are both descriptions of groups, but they represent different groups.

A parameter is a number that is a property of the population. Sometimes, when the population is small enough, there is no need to take a sample, and so determining a parameter is easier and a more accurate reflection of the population. A statistic is a number that represents a property of the sample. The statistic is an estimate of a population parameter.

Example 2There are 100 Senators in the U.S. Senate. 20 Senators voted against a bill last month. This number is an example of a parameter, because it is a number that represents the whole population.

There are 12,000 people at a football stadium. You want to determine the average number of miles people drove to the stadium. Instead of surveying the whole populationof 12,000 people, you randomly choose 1000 people as your sample. The average number of miles driven to the stadium by the sample is an example of a statistic.

Question Thomas wants to estimate the mean height of students attending his college. He records the heights of 25 randomly selected students attending the college. What is the parameter?

the heights of the randomly selected students

the mean height of all students attending the college

the mean height of the randomly selected students

the 25 randomly selected students

all the students attending the college

Question A 2016 Pew Research poll estimated the proportion of people supporting each presidential candidate in the fall election. They based their estimates on telephone interviews of 2,010 adults living in all 50 U.S. states. They asked each participant which presidential and vice presidential candidate they support, and used that data to calculate the proportions. What is the statistic in this experiment?

The candidate each participant supports.

The number of people Pew Research interviews.

The number of people in the United States.

The proportions of participants who support each presidential candidate.

The proportions of U.S. adults who support each presidential candidate.

Question Which of the following represents the population in the scenario below?

A researcher wants to know what percentage of people who live in Germany are satisfied with their government. Surveys are sent to people who live in the city limits of Berlin, Frankfurt, and Munich of Germany.

People who live in Europe

People who live in Germany

People who live in Berlin, Frankfurt, or Munich

People who live in Berlin

Statistics and Data

This video will define and contextualize key terminology including:

â€¢ Population: entire group of people/things under research

â€¢ Sample: a subset, or smaller portion of the population

â€¢ Variable: element, feature, or factor that is liable to vary or change.

â€¢ Data: values of variables

Question Susan wants to estimate the mean number of siblings for each student in her school. She records the number of siblings for each of 200 randomly selected students in the school. What is the population?

the specific number of siblings for each randomly selected student

all the students in the school

the mean number of siblings for all students in the school

the 200 randomly selected students

the mean number of siblings for the randomly selected students

Question Annie wants to estimate the percentage of homeowners who own at least one dog. She surveys 75randomly selected individuals to determine whether or not they own dogs. What is the population?

the 75 homeowners surveyed

specific responses to the survey

the percentage of surveyed homeowners who own at least one dog

the percentage of all homeowners who own at least one dog

all homeowners

Question There are 6000 people who attended a political debate at a convention center. There are three candidates who are participating in the debate – Mr. Smith, Mr. Jones, or Ms. Roberts. You want to find out which candidate is most popular amongst the people attending. You ask 500 people as they walk into the convention center.

Which represents the population in this scenario?

The three candidates – Mr. Smith, Mr. Jones, and Ms. Roberts

The 500 people surveyed

The 6000 people attending the debate

Everyone who has been the convention center that month

Question You want to find the average test score of the students in every math class in 11th grade. There are 15math classes in 11th grade. You survey the scores of 7 math classes, and you calculate that the average test score is 83%.

Which of the following represent the sample and the parameter in this scenario?

Sample: 7 math classes

Parameter: There is no parameter in this scenario.

Sample: 7 math classes

Parameter: the average test score of 83%

Sample: 15 math classes

Parameter: There is no parameter in this scenario.

Sample: 15 math classes

Parameter: the average test score of 83%

Statistics and Data

The science of statistics deals with the collection, analysis, interpretation, and presentation of data. We see and use data in our everyday lives.

In statistics, we generally want to study a population. A population is a total collection of persons, things, or objects under study. Gathering information about an entire population often costs too much or is virtually impossible. Instead, we collect a sample of the population or a smaller portion of the larger population. This is usually easier to do, and gives us a good idea of what’s going on in the population. A sample should have the same characteristics as the population it is representing.

Data are information about populations or samples. Generally, there are unknown characteristics, or variables, about a population that we wish to know. To obtain this information, we collect data by sampling some members of a population. Once collected, the data are used as the actual values of the variables. Data may be numbers (quantitative data) or they may be words (qualitative data).

Example 1 You want to determine the overall grade point average (GPA) at your school. There are 1800 students at your school. Since you want to collect data about all of the students, all 1800 students is the population. The variable is overall GPA at your school.

But, it would be difficult to ask every single one of the 1800 students in your school about his/her GPA. So, it would make sense to gain information from a smaller group of students who attend your school. So, you survey 200 random students. This portion of the population is called the sample.

The grade point averages of the students surveyed would be the data collected.

A statistic and a parameter are both descriptions of groups, but they represent different groups.

A parameter is a number that is a property of the population. Sometimes, when the population is small enough, there is no need to take a sample, and so determining a parameter is easier and a more accurate reflection of the population. A statistic is a number that represents a property of the sample. The statistic is an estimate of a population parameter.

Example 2 There are 100 Senators in the U.S. Senate. 20 Senators voted against a bill last month. This number is an example of a parameter, because it is a number that represents the whole population.

There are 12,000 people at a football stadium. You want to determine the average number of miles people drove to the stadium. Instead of surveying the whole populationof 12,000 people, you randomly choose 1000 people as your sample. The average number of miles driven to the stadium by the sample is an example of a statistic.

Question Patrick wants to estimate the percentage of parents who use cloth diapers. He asks a randomly selected group of 125 parents whether or not they use cloth diapers. What is the statistic?

the 125 people surveyed

the percentage of all parents who use cloth diapers

the percentage of surveyed parents who use cloth diapers

all parents who use cloth diapers

specific “yes” or “no” responses to the survey

Question Nick wants to estimate the percentage of homeowners that own at least one dog. He surveys 150randomly selected individuals to determine whether or not they own dogs. What is the sample?

the percentage of surveyed homeowners that own at least one dog

all homeowners

the percentage of all homeowners that own at least one dog

specific responses to the survey

the 150 homeowners surveyed

Question What term refers to all individuals, objects, or measurements whose properties are being studied?

population

variable

statistic

data

Question Joseph wants to estimate the mean number of siblings for each student in his school. He records the number of siblings for each of 200 randomly selected students in the school. What is the sample?

all the students in the school

the 200 randomly selected students

the mean number of siblings for the randomly selected students

the specific number of siblings for each randomly selected student

the mean number of siblings for all students in the school

Question Is the statement below true or false?

A parameter is a number that is used to represent a population characteristic and generally cannot be determined easily.

True

False

Question A 2016 Pew Research poll estimated the proportion of people supporting each presidential candidate in the fall election. They based their estimates on telephone interviews of 2,010 adults living in all 50 U.S. states. They asked each participant which presidential and vice presidential candidate they support, and used that data to calculate the proportions. What is the statistic in this experiment?

The candidate each participant supports.

The number of people Pew Research interviews.

The number of people in the United States.

The proportions of participants who support each presidential candidate.

The proportions of U.S. adults who support each presidential candidate.

Question Which of the following represents the population in the scenario below?

A researcher wants to know what percentage of people who live in Germany are satisfied with their government. Surveys are sent to people who live in the city limits of Berlin, Frankfurt, and Munich of Germany.

People who live in Europe

People who live in Germany

People who live in Berlin, Frankfurt, or Munich

People who live in Berlin

Statistics and Data

This video will define and contextualize key terminology including:

â€¢ Population: entire group of people/things under research

â€¢ Sample: a subset, or smaller portion of the population

â€¢ Variable: element, feature, or factor that is liable to vary or change.

â€¢ Data: values of variables

Question Matthew wants to estimate the mean height of students attending his college. He records the heights of 100 randomly selected students attending the college. What is the population?

the mean height of the randomly selected students

the mean height of all students attending the college

the 100 randomly selected students

all the students attending the college

the heights of the randomly selected students

Question Is the statement below true or false?

A variable is a characteristic of interest for each person or object in a population.

True

False

Question Is the statement below true or false?

Data is a subset of the population studied.

True

False

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