CTJan27 Online Year 6 - Defining and Identifying Random Sampling Techniques

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CTJan27 Online Year 6 - Defining and Identifying Random Sampling Techniques

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Multiple Choice

What is a 'population' in statistics?
A small group of individuals selected for a study.
The specific data collected during an experiment.
The entire group of individuals or objects that a researcher wants to study.
A summary of numerical information.
What is a 'sample' in statistics?
A complete list of all possible outcomes.
The total number of items in a large group.
A smaller, representative group chosen from a larger population.
A conclusion drawn from an experiment.
Why is it often necessary to study a 'sample' instead of an entire 'population'?
Studying a sample is usually more complex and takes longer.
Populations are too small to provide meaningful data.
Populations can be too large, expensive, or time-consuming to study completely.
Samples always give more accurate results than populations.
A principal wants to know if students at her school like the new lunch menu. She asks 100 students out of 1000 total students. What is the 'population' in this study?
All 1000 students at her school.
The new lunch menu itself.
The 100 students who were asked.
The principal of the school.
A principal wants to know if students at her school like the new lunch menu. She asks 100 students out of 1000 total students. What is the 'sample' in this study?
The 100 students who were asked.
The new lunch menu itself.
The school's cafeteria staff.
All 1000 students at her school.
What does it mean for a statistical sample to be 'biased'?
The results from the sample are easy to interpret.
Every member of the population has an equal chance of being selected.
The sample is perfectly representative of the population.
The sample does not accurately represent the population, leading to unfair or incorrect conclusions.
Which characteristic is essential for a sample to be considered truly 'random'?
Every member of the population has an equal and independent chance of being selected.
Selection is based on specific characteristics like age or location.
Only people who agree with the researcher's opinion are included.
The sample includes only the most accessible individuals.
Besides being random, what is another important characteristic of a useful sample?
It should only include data that supports a specific hypothesis.
It should be as small as possible to save time.
It should be selected by the person conducting the survey.
It should be representative of the entire population.
A teacher wants to select 5 students randomly from a class of 30. Which method demonstrates Simple Random Sampling (SRS)?
Picking the 5 students with the highest grades.
Choosing the first 5 students who arrive at class.
Selecting 5 students whose names start with a specific letter.
Writing each student's name on a slip of paper, putting them in a hat, and drawing 5 names without looking.
Which scenario describes a Simple Random Sample?
A store manager surveys customers who are shopping on a Tuesday afternoon.
A school principal assigns each of 500 students a number and uses a random number generator to pick 50 students.
A student asks only their friends for their opinion on a school project.
A researcher chooses the first 20 people he sees in a park.
A local newspaper wants to know readers' opinions on a new city park. They ask people to call in or email their thoughts. Is this a random sample (meaning unbiased and representative)?
Yes, because it's easy for people to participate.
No, because only people with strong opinions or those who choose to participate will respond.
No, because only people who read the newspaper can respond.
Yes, because everyone has a chance to call in.
A researcher wants to know the average height of all students in a large school. He measures the height of only the students on the basketball team. Is this a random sample (meaning unbiased and representative of *all* students)?
No, because basketball players are likely taller than the average student, making the sample biased.
No, because they are easy to find and measure quickly.
Yes, because basketball players are students.
Yes, because he measured all members of the team.
To get student opinions on a new school policy, a principal puts the names of all 800 students into a large drum and draws out 50 names to survey. Is this a random sample?
No, because it might not include students from every grade level.
Yes, because the principal is a fair person.
Yes, because every student had an equal chance of being selected for the survey.
No, because 50 students is too small a number.
A survey asks people walking past a gym about their exercise habits. Why might this sample be biased if the goal is to understand the exercise habits of the *general population*?
Not everyone walks past a gym.
People near a gym are more likely to exercise, so the sample wouldn't represent the general population.
It's a quick way to collect data.
People walking past a gym are generally more representative.
What is the main problem with using a biased sample in a study?
It leads to conclusions that are not accurate or fair for the entire population.
It means the data collected is difficult to read.
It causes the results to be too complex to analyze.
It makes the study take longer to complete.
Which of the following is an example of a 'population'?
All licensed drivers in a particular state.
A list of the top 10 songs on the radio.
10 people surveyed about their favorite movie.
The results of a survey about local elections.
Which of the following is an example of a 'sample'?
All the trees in a national park.
Every single student enrolled in a university.
The total number of registered voters in a city.
50 randomly selected residents from a town of 5,000 people.
A toy company wants to know if children like their new robot toy. They send surveys to 100 parents who purchased the toy online. Is this a random sample of *all children*?
Yes, because the parents bought the toy, so their children definitely played with it.
No, because it excludes children who did not have parents purchase the toy online, potentially biasing the results.
No, because the survey is sent only to parents who already bought the toy, so their children are more likely to like it.
Yes, because 100 parents is a large enough group.
A mayor wants to know how citizens feel about building a new community center. She decides to survey 200 citizens. What is the *best* way to ensure her sample is random?
Survey the first 200 people she sees at the grocery store.
Post a survey on social media and take the first 200 responses.
Ask 200 of her friends and family members.
Obtain a list of all citizens and use a random number generator to select 200 names for the survey.
Why is it important for a sample to be random when conducting a statistical study?
Random samples are easier to analyze and understand.
Random samples always produce a smaller amount of data.
Non-random samples are always much faster to collect.
A random sample helps ensure the results are unbiased and can be generalized to the entire population.
A school principal wants to understand the average amount of time Grade 8 students spend on homework each night. There are $300$ Grade 8 students in the school. The principal decides to ask the $30$ students who arrive earliest to school on Monday morning. What is the most significant statistical issue with this sampling method?
Asking only on Monday morning doesn't represent other days of the week.
The sample size of $30$ is too small for a population of $300$ students.
The students might not accurately recall their homework time.
Students who arrive earliest might have different homework habits than the general student population, introducing bias.
A local library wants to determine the most popular genre of books among its registered adult members, who number $12,500$. They decide to survey $100$ members by selecting every $125$th name from an alphabetically ordered list of all registered members. Which of the following statements best describes the sample and the sampling method used?
The sample is $100$ people, and the method is simple random sampling.
The sample is $100$ people, and the method is systematic random sampling.
The sample is $100$ people, and the method is a biased selection process.
The sample is the library's adult members, and the method is convenience sampling.
Why is it often necessary to select a sample from a population rather than surveying the entire population, especially when dealing with very large groups?
Surveying the entire population can be impractical, too costly, or too time-consuming, making sampling a more feasible approach.
It eliminates the possibility of human error in data collection.
It guarantees more accurate results because smaller groups are easier to manage.
It prevents the data from being manipulated by external factors.
A town council wants to gauge public opinion on building a new park. They place a survey on the town's official website and allow any resident to submit their responses. What type of bias is most likely to affect the results of this survey?
Non-response bias, because not everyone will choose to complete the survey.
Measurement bias, because the questions might be phrased unfairly.
Selection bias, because only residents with internet access can participate.
Voluntary response bias, because individuals with strong opinions are more likely to participate, distorting the overall representation.
Which of the following scenarios best describes a situation where a simple random sample (SRS) has been effectively implemented?
A researcher wants to study reading habits and surveys $50$ people walking out of a bookstore.
A company surveys its employees by choosing $20$ people who work on the top floor and $20$ people who work on the ground floor.
To select $10$ students from a class of $30$, each student's name is written on an identical slip of paper, placed in a hat, mixed thoroughly, and $10$ names are drawn without looking.
A teacher wants to know if students prefer group work or individual assignments, so she asks her most talkative students.
A restaurant manager wants to test a new menu item. For two weeks, every customer who orders a main course is given a short survey about the new item. The manager concludes that the new item is highly popular. What is the most significant limitation of this sampling method?
Customers who did not order a main course were excluded from the survey.
The survey was only conducted for two weeks, which might not be long enough.
The customers might not have enough experience with the new item to give a valid opinion.
Only customers who *choose* to eat at the restaurant (and order a main course) are included, potentially biasing the results towards those who already like the restaurant's food.
In a study, a researcher is trying to determine if eating breakfast improves test scores for Grade 8 students. They survey $100$ students from a specific high-achieving math class. Why is this sampling method considered biased for a general conclusion about *all* Grade 8 students?
The sample size of $100$ is too small to draw any meaningful conclusions.
High-achieving math students are not representative of the entire population of Grade 8 students, introducing selection bias.
Surveying students about breakfast habits is difficult to do accurately.
Students in a specific math class might already have similar eating habits.
What is the primary characteristic that distinguishes a random sample from a non-random (biased) sample?
A random sample is collected more quickly than a non-random sample.
A random sample is always larger than a non-random sample.
In a random sample, every member of the population has an equal, non-zero chance of being selected, minimizing systematic favoritism.
A random sample uses technology, while a non-random sample does not.
A town council needs to select $50$ residents for a focus group on a new zoning plan. They have a complete list of all $5,000$ registered voters. Which of the following methods would introduce the most significant bias into their selection?
Publicly announcing the focus group and taking the first $50$ volunteers.
Selecting every $100$th person from the alphabetically ordered list of voters.
Selecting $50$ residents from a single neighborhood known for its strong opinions on zoning.
Using a random number generator to pick $50$ numbers corresponding to the voter list.
To ensure a sample is truly random and representative of a large population, what is the *most crucial* step an individual must take before applying a selection method like a random number generator?
Obtain a complete and accurate list of every individual member within the target population.
Determine the exact number of people to be included in the sample.
Prepare a detailed list of questions for the survey.
Recruit trained interviewers to conduct the data collection.
A music teacher wants to know the most preferred instrument among students in her school. She decides to survey $20$ students. Which sampling method is most likely to produce a biased result?
Asking only the students who are currently enrolled in the advanced band class.
Assigning each student a number and using a random number generator to pick $20$ students.
Selecting the first $20$ students who enter the music room on a given Monday morning.
Drawing $20$ names from a hat containing the names of all students in the school.
A marketing company conducts a survey by calling landline phone numbers randomly generated across a city. They then ask to speak to the adult (over $18$) in the household whose birthday is next. What specific characteristic of simple random sampling is this method attempting to achieve within each contacted household, even if the overall city sampling has other limitations?
To ensure the sample size is manageable.
To reduce the cost of the survey by limiting interactions.
To give every eligible adult in the household an equal chance of being selected, once the household is reached.
To prevent multiple people from the same household from participating.
Which of the following statements about statistical bias is FALSE?
A biased sample does not accurately represent the characteristics of the population.
Bias in a sample can lead to inaccurate conclusions about the population.
Increasing the sample size of a biased sample will always correct the bias.
Bias can be introduced unintentionally through the sampling method or questionnaire design.
A clothing store wants to know the average shoe size of its male customers. For one week, they record the shoe size of every $10$th male customer who makes a purchase. What is the most likely population being sampled here, and what is a potential source of bias?
The population is male customers who purchase shoes; bias because it's only for one week.
The population is all customers; bias because only shoe size is recorded.
The population is male customers who make a purchase; bias because only customers who make a purchase are included, potentially excluding those who just browse or have unusual sizes not in stock.
The population is all male customers; bias because not all male customers make a purchase.
A student researcher wants to study the sleeping habits of teenagers in their high school, which has $1,200$ students. The researcher plans to survey $100$ students. They decide to ask their $100$ closest friends. Why is this sampling method fundamentally flawed, even if the researcher believes their friends are 'typical' teenagers?
Friends might be reluctant to share their true sleeping habits with the researcher.
Friends tend to share similar characteristics and lifestyles, making them an unrepresentative subset and introducing selection bias.
The researcher might unintentionally influence their friends' responses.
The sample size of $100$ friends is too small to represent $1,200$ students.

Numerical

A high school has $850$ students. To understand student opinions on cafeteria food, a random sample of $85$ students is selected to complete a survey. How many students in the high school are *not* included in this sample?
In a Grade $8$ class, there are $25$ students. The teacher decides to select one student for a special task using Simple Random Sampling (SRS), where each student's name is written on a separate slip of paper and one is drawn. For any specific student, what is the value in the denominator of the probability fraction representing their chance of being chosen?
A city council wants to survey $5\%$ of its $12,000$ adult residents to understand their views on a new park project. If they use a random sampling method, how many residents should be included in their sample?
A group of $48$ people needs to have $1$ person selected using Simple Random Sampling. If each person's name is written on a unique piece of paper and put into a hat, how many pieces of paper will be in the hat before the selection is made?
A company has $300$ employees. The CEO wants to survey employees about their job satisfaction but only sends the survey to the $120$ employees in the marketing department, assuming they represent everyone. How many employees are automatically excluded from the possibility of being surveyed by this *biased* method?

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CTJan27 Online Year 6 - Defining and Identifying Random Sampling Techniques

Multiple Choice

Numerical