Master Sampling and Sampling Distributions in Data Analytics

Question 1

Which type of stratified sampling involves dividing the population into strata of equal size?

Accepted Answer

Proportional stratified sampling

Answer

Disproportionate stratified sampling

Answer

Cluster sampling

Answer

Systematic sampling

Question 2

The purpose of sampling in data analytics is to:

Accepted Answer

Obtain information about a population from a smaller subset

Answer

Reduce the cost of data collection

Answer

Make data analysis more efficient

Answer

Improve the accuracy of data analysis

Question 3

The difference between a population and a sample is that:

Accepted Answer

A population is the entire group of individuals being studied, while a sample is a subset of the population

Answer

A population is the subset of individuals being studied, while a sample is the entire group

Answer

A population is the group of individuals that are interested in the study, while a sample is the group of individuals that are actually studied

Answer

A population is the group of individuals that are available for study, while a sample is the group of individuals that are actually studied

Question 4

If a class has 20 students, including 12 male students, the probability of selecting a male student from the class is:

Accepted Answer

0.6

Answer

0.5

Answer

0.7

Answer

0.8

Question 5

What is the key distinction between a parameter and a statistic?

Accepted Answer

A parameter is a population characteristic, while a statistic is a sample characteristic

Answer

A statistic is a population characteristic, while a parameter is a sample characteristic

Answer

Parameters are always known, while statistics are always estimated

Answer

Statistics are always known, while parameters are always estimated

Question 6

What is the standard error of the mean (SEM) used to estimate?

Accepted Answer

The standard deviation of the sample mean

Answer

The standard deviation of the population mean

Answer

The standard deviation of the sample

Answer

The standard deviation of the population

Question 7

Which of the following is **not** an ethical consideration in sampling?

Accepted Answer

Purposeful deception

Answer

Informed consent

Answer

Confidentiality

Answer

Respect for privacy

Question 8

According to the central limit theorem, as the sample size increases, what happens to the sampling distribution of the sample mean?

Accepted Answer

It becomes more normally distributed

Answer

It becomes more skewed

Answer

Its standard deviation decreases

Answer

Its standard deviation increases

Question 9

Which sampling method is generally considered to produce the most representative sample in data analytics?

Accepted Answer

Simple random sampling

Answer

Convenience sampling

Answer

Quota sampling

Answer

Snowball sampling

Question 10

What is the key distinction between a parameter and a statistic in data analytics?

Accepted Answer

A parameter represents a population characteristic, while a statistic represents a sample characteristic

Answer

A statistic represents a population characteristic, while a parameter represents a sample characteristic

Answer

Parameters are always known, while statistics are always estimated

Answer

There is no difference between a parameter and a statistic

Question 11

According to the empirical rule, what is the probability of obtaining a sample mean that is within two standard errors of the population mean?

Accepted Answer

0.9544

Answer

0.6826

Answer

0.9973

Answer

1.0000

Question 12

Which of the following is NOT a potential source of bias in sampling?

Accepted Answer

Sampling error

Answer

Sampling frame error

Answer

Self-selection bias

Answer

Non-response bias

Question 13

An unbiased estimate of the population standard deviation is provided by:

Accepted Answer

Sample variance

Answer

Sample mean

Answer

Population mean

Answer

Population variance

Question 14

In convenience sampling, the sample is selected based on:

Accepted Answer

Researcher's judgment and knowledge

Answer

Random selection

Answer

Stratification

Answer

Systematic selection

Question 15

According to the central limit theorem, the sampling distribution of the sample mean will be approximately normal if the sample size is:

Accepted Answer

Large enough

Answer

Small

Answer

Equal to the population size

Answer

Always normal regardless of sample size

Question 16

In cluster sampling, the population is divided into:

Accepted Answer

Clusters

Answer

Strata

Answer

Segments

Answer

Groups

Question 17

When selecting a sampling method, the most important factor to consider is:

Accepted Answer

Research objectives

Answer

Cost

Answer

Time constraints

Answer

Data availability

Question 18

Which of the following is NOT considered a probability sampling method?

Accepted Answer

Convenience sampling

Answer

Random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Question 19

What is a key assumption of the central limit theorem?

Accepted Answer

The sample size is sufficiently large.

Answer

The population mean is known.

Answer

The sampling method is unbiased.

Answer

The population distribution is normal.

Question 20

What is the shape of the sampling distribution of sample means when the population distribution is approximately normal?

Accepted Answer

Approximately normal

Answer

Uniform

Answer

Skewed

Answer

Exponential

Question 21

What is a primary benefit of using stratified sampling?

Accepted Answer

Increased precision of population estimates

Answer

Convenience

Answer

Reduced sample size

Answer

Lower cost

Question 22

What is the fundamental purpose of a confidence interval?

Accepted Answer

To estimate the population parameter with a specified level of confidence

Answer

To determine the sample size for a study

Answer

To test hypotheses about the population

Question 23

Which condition is necessary when conducting a two-sample t-test?

Accepted Answer

Independent samples with approximately normal distributions.

Answer

Known population variances

Answer

Equal sample sizes

Question 24

A researcher wants to test the hypothesis that a particular preparation course improves the standardized test scores of students who take it. Which type of sampling method would be most appropriate for this study?

Accepted Answer

Randomized controlled trial

Answer

Cluster sampling

Answer

Quota sampling

Answer

Convenience sampling

Question 25

Which of the following is NOT a type of probability sampling method?

Accepted Answer

Convenience sampling

Answer

Stratified sampling

Answer

Systematic sampling

Answer

Cluster sampling

Question 26

What is the main purpose of using a sampling distribution?

Accepted Answer

To estimate the distribution of a population parameter based on sample data.

Answer

To test hypotheses about the population parameter.

Answer

To describe the variability within a sample.

Question 27

According to the central limit theorem, as the sample size increases, the sampling distribution of the sample mean:

Accepted Answer

Approaches a normal distribution, regardless of the shape of the population distribution.

Answer

Has a wider variance.

Answer

Becomes more skewed.

Question 28

A confidence interval is used to:

Accepted Answer

Estimate the true population parameter with a specified level of confidence.

Answer

Test hypotheses about a population parameter.

Answer

Determine the sample size needed for a given study.

Question 29

The confidence level of a confidence interval represents the:

Accepted Answer

Probability that the true population parameter lies within the interval.

Answer

Margin of error for the sample.

Answer

Probability that the sample mean is equal to the population mean.

Question 30

Which of the following factors primarily affects the width of a confidence interval?

Accepted Answer

Sample size and confidence level.

Answer

Population mean and population standard deviation.

Answer

Skewness and kurtosis of the population distribution.

Answer

Sampling method and type of data.

Question 31

Which of the following is a potential limitation of sampling?

Accepted Answer

Sampling error, which can lead to bias and inaccurate estimates.

Answer

Timeliness in obtaining results.

Answer

Cost-effectiveness compared to a census.

Answer

Flexibility in selecting the sample.

Question 32

A researcher aims to study the spending habits of high-income individuals in a particular region. Which sampling method would be most appropriate to ensure a representative sample?

Accepted Answer

Stratified random sampling

Answer

Convenience sampling

Answer

Snowball sampling

Answer

Simple random sampling

Question 33

A company conducts a survey to estimate the proportion of customers who are satisfied with their service. They randomly select 400 customers from their database and find that 320 are satisfied. Calculate the sample proportion of satisfied customers.

Accepted Answer

0.8

Answer

0.2

Answer

320

Answer

400

Question 34

Which of the following is NOT a characteristic of a sampling distribution?

Accepted Answer

It always follows a normal distribution.

Answer

It has a standard deviation called the standard error of the mean.

Answer

It is a theoretical distribution that represents the distribution of all possible sample means.

Answer

Its mean is equal to the population mean.

Question 35

A company wants to estimate the average time it takes to complete a specific task. They randomly sample 36 employees and find the average completion time is 25 minutes with a standard deviation of 5 minutes. Calculate the standard error of the mean.

Accepted Answer

0.83 minutes

Answer

5 minutes

Answer

25 minutes

Answer

1.25 minutes

Question 36

A researcher aims to estimate the average height of students at a university. They randomly select 100 students and find the average height is 170 cm. Based on the Central Limit Theorem, what can be concluded about the sampling distribution of the sample mean?

Accepted Answer

It will be approximately normally distributed with a mean of 170 cm.

Answer

The distribution cannot be determined without knowing the population standard deviation.

Answer

It will be skewed with a mean of 170 cm.

Answer

It will be exactly normally distributed with a mean of 170 cm.

Question 37

Which sampling method is most likely to produce a biased sample?

Accepted Answer

Convenience sampling

Answer

Simple random sampling

Answer

Stratified random sampling

Answer

Systematic sampling

Question 38

A researcher investigates the impact of a new advertising campaign on customer satisfaction. They compare the satisfaction levels of a group of customers who saw the campaign to a group who did not. This is an example of:

Accepted Answer

Experimental sampling

Answer

Convenience sampling

Answer

Cluster sampling

Answer

Simple random sampling

Question 39

A company wants to estimate the average number of hours employees work per week. They randomly sample 50 employees and find the average is 40 hours with a standard deviation of 5 hours. Calculate the 95% confidence interval for the population mean.

Accepted Answer

39.02 to 40.98 hours

Answer

40 to 45 hours

Answer

35 to 45 hours

Answer

38.5 to 41.5 hours

Question 40

A researcher wants to test the hypothesis that the average age of MBA students is 28 years. They randomly sample 100 MBA students and find the average age is 27 years with a standard deviation of 2 years. What can be said about the p-value for this hypothesis test?

Accepted Answer

The p-value cannot be determined without knowing the significance level.

Answer

The p-value is 0.05.

Answer

The p-value is greater than 0.10.

Answer

The p-value is 0.10.

Question 41

Which of the following is NOT a type of probability sampling method?

Accepted Answer

Convenience sampling

Answer

Stratified sampling

Answer

Systematic sampling

Answer

Cluster sampling

Question 42

The central limit theorem states that as the sample size increases, the shape of the sampling distribution of the sample mean approaches:

Accepted Answer

A normal distribution

Answer

A Poisson distribution

Answer

The original population distribution.

Answer

A uniform distribution

Question 43

A researcher wants to estimate the average weight of apples in a large orchard. They randomly select 100 apples. What is the probability that the sample mean weight will be within 1 pound of the true population mean? (Assume a normal distribution and a known population standard deviation.)

Accepted Answer

This probability cannot be calculated without knowing the population standard deviation.

Answer

0.75

Answer

0.25

Answer

0.95

Question 44

Which of the following is a potential drawback of cluster sampling?

Accepted Answer

Increased sampling error within clusters

Answer

Reduced cost and effort

Answer

Ease of implementation

Answer

Increased representativeness

Question 45

In the context of sampling distributions, the standard deviation is known as the:

Accepted Answer

Standard error of the mean

Answer

Standard deviation of the population

Answer

Margin of error

Answer

Confidence interval

Question 46

A company with a comprehensive customer database intends to conduct a survey to gauge customer satisfaction. Which sampling method is most suitable for this scenario?

Accepted Answer

Simple random sampling

Answer

Cluster sampling

Answer

Stratified sampling

Answer

Quota sampling

Question 47

Which assumption is fundamental to the central limit theorem?

Accepted Answer

Random selection of the sample

Answer

Known standard deviation of the population

Answer

Normal distribution of the population

Answer

Large sample size

Question 48

A researcher posits that the mean height of college students is 68 inches. A sample of 50 students yields an average height of 69 inches with a standard deviation of 2 inches. Assuming the null hypothesis, what is the probability of obtaining this sample mean?

Accepted Answer

0.0228

Answer

0.2112

Answer

0.0528

Answer

0.1056

Question 49

When making inferences about a population parameter, what is the primary purpose of confidence intervals?

Accepted Answer

To provide an estimated range within which the true parameter is likely to lie

Answer

To minimize the likelihood of a Type I error

Answer

To definitively determine the exact value of the parameter

Question 50

For a simple random sample to be valid, which criterion must be met?

Accepted Answer

Every member of the population has an equal chance of being included in the sample.

Answer

The sample size must be sufficiently large.

Answer

The population must be normally distributed.