Module 3: Sampling

Q: Which of the following scenarios would benefit from replacing their current sample with a representative sample? Select all that apply.

• A researcher conducts a survey on the experience of high school students. For their sample, they choose students from a variety of academic, social, and cultural backgrounds.
• A researcher conducts a survey on computer skills among university students. For their sample, they choose students who major in computer science. 
• A researcher conducts a poll for an upcoming national election. For their sample, they choose voters from a single city. 
• A researcher conducts an employee satisfaction survey for a company. For their sample, they choose employees who have worked at the company for at least 25 years. 

Explanation: This scenario seems to already be working toward the goal of achieving a representative sample by adding students who come from a variety of different backgrounds. There is a possibility that the sample does not need replacement since it seems to be typical of the whole. This sample is significantly skewed toward students majoring in computer science, and it does not accurately reflect the whole student body at the institution. To generalize the results about computer abilities across all university students, it is necessary to have a sample that is representative of the student body and includes students from a variety of majors. Within the context of this case, it would be beneficial to replace the existing sample with a representative sample. Because of disparities in demographics, political leanings, and other variables, it is very improbable that a single city would be able to accurately reflect the whole national electorate. To effectively evaluate election feelings on a national level, it is necessary to collect a sample that is typical of the whole country. Within the context of this case, it would be beneficial to replace the existing sample with a representative sample.

Q: Fill in the blank: In statistics, _____ refers to the number of individuals or items chosen for a study or experiment.

• target population
• sampling frame
• sample size 
• sampling method

Explanation: In the field of statistics, the term "sample size" refers to the number of people or things that are selected for an investigation or experiment.

Q: Which of the following statements accurately describe non-probability sampling? Select all that apply.

• Non-probability sampling typically uses random selection.
• Non-probability sampling is often based on convenience. 
• Non-probability sampling is often based on the personal preferences of the researcher. 
• Non-probability sampling can result in biased samples. 

Q: Which sampling method involves dividing a population into groups and randomly selecting some members from each group for the sample?

• Simple random sampling
• Stratified random sampling 
• Systematic random sampling
• Cluster random sampling

Explanation: The technique of sampling known as stratified random sampling includes dividing a population into groups and then choosing some individuals at random from each of those categories to make up the sample.

Q: Which sampling method involves choosing members of a population who are easy to contact or reach?

• Voluntary response sampling
• Convenience sampling 
• Purposive sampling
• Snowball sampling

Explanation: Convenience sampling is a type of sampling that includes selecting individuals of a population that are simple to contact or reach throughout the sample process.

Q: Fill in the blank: Standard error measures the _____ of a sampling distribution.

• standard deviation
• mode
• median
• mean

Explanation: One way to quantify the standard deviation of a sample distribution is via the use of standard error.

Q: What concept states that the sampling distribution of the mean approaches a normal distribution as the sample size increases?

• Sampling frame
• Central limit theorem 
• Bayes’ theorem
• Standard error

Explanation: The central limit theorem is a notion that claims that as the sample size rises, the sampling distribution of the mean will approach a normal distribution that is more similar to the normal distribution.

Q: A data professional is working with data about annual household income. They want to use Python to simulate taking a random sample of income values from the dataset. They write the following code: sample(n=100, replace=True, random_state=230). What is the sample size of the random sample?

• 100 
• 230
• 23
• 10

Explanation: There is a random sample in the code sample(n=100, replace=True, random_state=230) that has a sample size of 100.

Q: Fill in the blank: A _____ sample accurately reflects the characteristics of a population.

• Representative 
• nonrepresentative
• biased
• very small

Explanation: A sample that is representative of a population properly represents the features of that group.

Q: What stage of the sampling process refers to creating a list of all the items in the target population?

• Determine the sample size
• Collect the sample data
• Select the sampling frame 
• Choose the sampling method

Explanation: Selecting the sampling frame is the step of the sampling process that refers to the act of establishing a list of all the things that are included in the population that is being sampled.

Q: Which of the following statements accurately describe a sampling distribution? Select all that apply.

• A sampling distribution is a probability distribution of a population parameter.
• A sampling distribution can be visualized with a histogram. 
• A sampling distribution represents the probability distribution of a statistic under random sampling. 
• The distribution of a sample mean and the distribution of a sample proportion are examples of sampling distributions. 

Explanation: A sampling distribution is a representation of the probability distribution of a statistic according to the use of random sampling. instances of sampling distributions include the distribution of a sample mean and the distribution of a sample proportion: both of these instances are distributions.

Q: A data professional is conducting an employee satisfaction survey. First, they list all the employees alphabetically by first name. Then, they randomly choose a starting point on the list and pick every third name to be in the sample. What sampling method are they using?

• Systematic random sampling 
• Cluster random sampling
• Simple random sampling
• Stratified random sampling

Explanation: This type of sampling is known as systematic random sampling, and it involves listing personnel in alphabetical order and selecting every third name beginning at a random point.

Q: Which of the following scenarios best describe snowball sampling?

• Researchers select members of a population who are easy to contact or reach.
• Researchers select members of a population based on random sampling.
• Researchers recruit initial participants to be in a study, then ask them to recruit other people to participate in the study. 
• Researchers select participants based on the purpose of their study.

Explanation: Researchers begin by recruiting initial volunteers to take part in the research, and then they ask those participants to recruit other individuals to take part in the study. Snowball sampling is a method of recruitment that involves individuals suggesting others to participate in the research, establishing a chain or "snowball" effect of recruitment recruitment.

Q: Which of the following statements accurately describe the standard error of the mean? Select all that apply.

• The higher the standard error, the more precise the sample mean is.
• The standard error of the mean measures variability among the sample means obtained in repeated sampling. 
• A larger standard error indicates that, in repeated sampling, the sample means are more spread out. 
• The lower the standard error, the more precise the sample mean is. 

Explanation: It is possible to assess the variability among the sample means acquired via repeated sampling by using the standard error of the mean. In repeated sampling, a greater standard error suggests that the sample averages are more dispersed than they may have been otherwise.

Q: Fill in the blank: The central limit theorem states that the _____ of the mean approaches a normal distribution as the sample size increases.

• sampling frame
• sampling variability
• sampling distribution 
• sampling bias

Explanation: As the sample size rises, the central limit theorem asserts that the sampling distribution of the mean will get closer and closer to a normal distribution.

Q: A data professional is working with data about annual household income. They want to use Python to simulate taking a random sample of income values from the dataset. They write the following code: sample(n=100, replace=True, random_state=230). What does the argument replace=True refer to?

• Sampling without replacement
• Sampling with replacement 
• Replacing decimal values with whole numbers
• Replacing whole numbers with decimal values

Explanation: In the code sample(n=100, replace=True, random_state=230), the insertion of the replace=True parameter indicates that the sampling method is replacement-based. Each observation in the population has an identical chance of being picked for the sample each time, and it can be selected more than once. This indicates that the probability of selection changes with time.

Q: Which of the following statements accurately describe a representative sample? Select all that apply.

• A representative sample represents some groups in the population but not others.
• A representative sample suffers from sampling bias.
• A representative sample reflects the characteristics of the overall population. 
• A representative sample helps data professionals make reliable inferences based on sample data.

Explanation: One definition of a representative sample is one that accurately represents the characteristics of the whole population. It is easier for data professionals to draw trustworthy conclusions based on sample data when they have access to a representative sample.

Q: Which of the following statements accurately describes the relationship between probability sampling and non-probability sampling?

• Probability sampling is more biased than non-probability sampling.
• Probability sampling is typically less expensive than non-probability sampling.
• Probability sampling gives data professionals a better chance of generating a representative sample than non-probability sampling. 
• Probability sampling is typically more convenient than non-probability sampling.

Explanation: When compared to non-probability sampling, probability sampling provides data professionals with a greater opportunity to generate a sample that is representative of the population. With the aid of probability sampling techniques, it is possible to generate samples that are representative of the population. These approaches are meant to guarantee that every component of the population has a known chance of being included in the sample.

Q: What is a key difference between stratified random sampling and cluster random sampling?

• Stratified sampling is a probability sampling method; cluster sampling is a non-probability sampling method.
• In stratified sampling, you randomly choose some members from each group to be in the sample; in cluster sampling, you choose all members from each group to be in the sample. 
• In stratified sampling, you randomly choose all members from each group to be in the sample; in cluster sampling, you choose some members from each group to be in the sample.
• Stratified sampling is a non-probability sampling method; cluster sampling is a probability sampling method.

Explanation: Involves first separating the population into groups that are similar to one another (known as strata) based on specific characteristics, and then performing a random selection of people from each stratum to include in the sample.entails first splitting the population into different groupings, sometimes known as clusters, and then picking complete clusters at random to be included in the sample.

Q: A data professional is working with data about annual household income. They want to use Python to simulate taking a random sample of income values from the dataset. They write the following code: sample(n=100, replace=True, random_state=230). What is the random seed?

• 100
• 230 
• 23
• 10

Explanation: 230 is the value of the random seed in the code sample (n=100, replace=True, random_state=230).

Q: The instructor of a fitness class asks their regular students to take an online survey about the quality of the class. What sampling method does this scenario refer to?

• Purposive sampling
• Convenience sampling
• Snowball sampling
• Voluntary response sampling 

Explanation: The term "convenience sampling" refers to the situation in which the teacher requests regularly attending students to participate in an online survey on the quality of the class. This approach comprises picking folks who are easily accessible or straightforward to get in touch with. In this particular instance, this pertains to the individuals who are frequent participants in the exercise class.

Q: A representative sample does not reflect the characteristics of a population.

• True
• False 

Explanation: A representative sample is one that correctly represents the features of a population. As a result, it offers a credible foundation for deriving conclusions about the population as a whole. Because of this, the assertion that "A representative sample does not reflect the characteristics of a population" is not true.