Welcome to the Content Review of Samples and Surveys.

Select the concepts or topics that you feel unsure about.

• Defining and identifying different types of samples

• Understanding bias in sampling

• The difference between population and sample

• Types of surveys and data collection methods

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CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

What is the best description of the term SAMPLE?

• a small group taken from the entire group

• the entire group that fits set criteria

• every possible sample of a given size has the exact same chance of being selected

• no interaction is made with the group/subject being studied

Answer explanation

A sample is a subset of a larger population that is selected to represent the whole. Researchers use samples because studying an entire population is often impractical or impossible. By analyzing a well-chosen sample, we can make inferences about the broader group while saving time and resources.

The other choices describe different concepts:

• "The entire group that fits set criteria" refers to the population, not the sample.

• "Every possible sample of a given size has the exact same chance of being selected" describes a simple random sample, which is a type of sampling method.

• "No interaction is made with the group/subject being studied" refers to an observational study, not the definition of a sample.

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CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

What is the best description of the term OBSERVATIONAL STUDY?

• a small group taken from the entire group

• the entire group that fits set criteria

• every possible sample of a given size has the exact same chance of being selected

• no interaction is made with the group/subject being studied

Answer explanation

The correct answer is "no interaction is made with the group/subject being studied."

An observational study is a type of research where data is collected without influencing or interfering with the subjects. Researchers simply observe and record information as it naturally occurs. This is different from an experiment, where researchers actively impose treatments or conditions on subjects to study the effects.

The other choices describe different concepts:

• "A small group taken from the entire group" refers to a sample rather than an observational study.

• "The entire group that fits set criteria" describes a population, not an observational study.

• "Every possible sample of a given size has the exact same chance of being selected" refers to a simple random sample, which is a sampling method, not a study type.

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CCSS.HSS.IC.B.3

What is the best description of the term POPULATION?

• no interaction is made with the group/subject being studied

• the entire group that fits set criteria

• every possible sample of a given size has the exact same chance of being selected

• systematic errors in the way the sample represents the population

Answer explanation

The correct answer is "the entire group that fits set criteria."

A population in statistics refers to the complete set of individuals, objects, or events that meet specific criteria for a study. It is the group from which a sample is drawn and about which conclusions are made. For example, if a study focuses on high school students in Virginia, the population would be all high school students in Virginia.

The other choices describe different concepts:

• "No interaction is made with the group/subject being studied" refers to an observational study, not a population.

• "Every possible sample of a given size has the exact same chance of being selected" describes a simple random sample, which is a sampling method.

• "Systematic errors in the way the sample represents the population" refers to bias, which affects the accuracy of a study but is not the definition of a population.

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

What is the best description of the term BIAS?

• no interaction is made with the group/subject being studied

• the entire group that fits set criteria

• every possible sample of a given size has the exact same chance of being selected

• systematic errors in the way the sample represents the population

Answer explanation

The correct answer is "systematic errors in the way the sample represents the population."

Bias in statistics occurs when a study or sampling method systematically favors certain outcomes, leading to results that do not accurately reflect the true population. Bias can occur in various ways, such as through poor sampling methods, leading questions in surveys, or nonresponse from certain groups. Reducing bias is crucial to ensuring the reliability of a study’s conclusions.

The other choices describe different concepts:

• "No interaction is made with the group/subject being studied" refers to an observational study, not bias.

• "The entire group that fits set criteria" defines a population, not bias.

• "Every possible sample of a given size has the exact same chance of being selected" describes a simple random sample, which is a way to reduce bias rather than define it.

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CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

What is the best description of the term SIMPLE RANDOM SAMPLE?

• no interaction is made with the group/subject being studied

• the entire group that fits set criteria

• every possible sample of a given size has the exact same chance of being selected

• systematic errors in the way the sample represents the population

Answer explanation

The correct answer is "every possible sample of a given size has the exact same chance of being selected."

A simple random sample (SRS) is a sampling method in which each individual and each possible subgroup of a specific size in the population has an equal chance of being chosen. This method helps eliminate bias and ensures that the sample is representative of the population. Common ways to conduct a simple random sample include using random number generators or drawing names from a hat.

The other choices describe different concepts:

• "No interaction is made with the group/subject being studied" refers to an observational study, not a sampling method.

• "The entire group that fits set criteria" defines a population, while a simple random sample is just a subset of the population.

• "Systematic errors in the way the sample represents the population" refers to bias, which is what a simple random sample aims to reduce.

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CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

Let's say I want to measure the amount of sleep students get per night and how it affects student grades.

Which of the following should not be considered because of bias?

• Survey sent to all students. Students have the option of returning the survey or not.

• A question in a survey asks "Responsible students get at least 8 hours of sleep per night. How many hours did you get last night?"

• 3 students were surveyed.

• All student names were put in a bowl and n names were selected to complete a survey.

Answer explanation

The answers that should not be considered due to bias are:

1. "Survey sent to all students. Students have the option of returning the survey or not."

   • This introduces nonresponse bias because students who choose to respond may differ significantly from those who do not. For example, students who get more sleep might be more likely to respond, leading to an unrepresentative sample.

2. "A question in a survey asks 'Responsible students get at least 8 hours of sleep per night. How many hours did you get last night?'"

   • This introduces response bias due to the wording of the question. By implying that responsible students get 8 hours of sleep, students may feel pressured to report more sleep than they actually got, skewing the results.

3. "3 students were surveyed."

   • This introduces sampling bias because the sample size is far too small to accurately represent the entire student population. A small sample may not capture the full range of sleep habits and their effects on grades.

The only choice that is not biased is:

• "All student names were put in a bowl and n names were selected to complete a survey."

  • This describes a simple random sample, which ensures that every student has an equal chance of being chosen, reducing bias.

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CCSS.HSS.IC.B.3

In this unit, which notation do you use for the size of a population?

• N

• n

• P

• p

Answer explanation

In statistics, N is used to represent the size of a population, meaning the total number of individuals or items in the entire group being studied.

The other choices represent different concepts:

• "n" represents the sample size, which is the number of individuals selected from the population for study.

• "P" typically represents the proportion of a population that has a certain characteristic.

• "p" usually represents the sample proportion, which is the proportion of a sample with a certain characteristic.

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CCSS.6.SP.B.5A

In this unit, which notation do you use for the size of a sample?

• N

• n

• S

• s

Answer explanation

In statistics, n represents the size of a sample, meaning the number of individuals selected from the population for a study.

The other choices represent different concepts:

• "N" represents the size of a population, which is the total number of individuals in the entire group being studied.

• "S" and "s" are not standard notations for sample size in this context. However, "s" is sometimes used to represent the sample standard deviation.

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CCSS.6.SP.B.5A

Which of these is the best way to create a sample of 20 people from which to collect data?

• Pick 20 people from your two favorite classes.

• Ask the first 20 people you see at your school theater performance.

• Put the names of all students from your school in a hat and without looking select 20 names.

• Send the questions to all students from your school and use the first 20 responses.

Answer explanation

✅ "Put the names of all students from your school in a hat and without looking select 20 names."

Explanation:

This method ensures a simple random sample, meaning every student in the school has an equal chance of being selected. This helps reduce bias and makes the sample more representative of the entire student population.

Why the other choices introduce bias:

• "Pick 20 people from your two favorite classes."

  • This introduces selection bias because students in those classes may not represent the entire school.

• "Ask the first 20 people you see at your school theater performance."

  • This introduces convenience bias, as it only includes students who attend the theater performance, which may not be representative of all students.

• "Send the questions to all students from your school and use the first 20 responses."

  • This introduces voluntary response bias, meaning only students who are highly motivated to answer will be included, which may not reflect the general student body.

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1