QCM : Introduction to Statistics and Sampling — 21 questions

Questions et réponses du QCM

1. Which sequence best represents the usual cycle of a statistical investigation?

Interpret results, organize a list, collect data, and stop
Collect data, publish results, pose a question, and discard data
Pose a question, collect data, analyze data, and interpret results
Analyze data, pose a question, interpret results, and collect data

Pose a question, collect data, analyze data, and interpret results

Explication

A statistical investigation commonly proceeds by posing a question, collecting data, analyzing the data, and interpreting the results. It is a cycle rather than a process that ends after making a list.

2. A researcher uses an advanced statistical method on data containing many inaccurate measurements. What is the most reasonable conclusion?

The method guarantees conclusions that are more accurate than the data
The method makes the quality of the original data irrelevant
The method’s conclusions may be limited by the poor-quality data
The method automatically corrects every inaccurate measurement

The method’s conclusions may be limited by the poor-quality data

Explication

A statistical procedure cannot be more accurate than the data or facts on which it is based. An advanced method does not automatically overcome unreliable data.

3. In a study of all employees at a company, what does one particular employee represent?

An individual
A variable
A population
A sample

An individual

Explication

An individual is one person or object included in a statistical study. The population would be every employee of interest, while a sample would be only some of them.

4. A school wants to study the opinions of every student enrolled at the school. Which group is the population?

Every student enrolled at the school
One student chosen by the principal
The students who answer the survey first
The students selected to answer a survey

Every student enrolled at the school

Explication

A population consists of every individual of interest in a statistical study. Here, that means all students enrolled at the school, not merely those included in a sample.

5. A researcher selects 200 voters from a city to estimate the opinions of all city voters. What do the 200 selected voters constitute?

A complete census
A sample
A variable
A population

A sample

Explication

A sample consists of only some of the individuals of interest. The 200 selected voters are a subset of the city’s entire population of voters.

6. Which description best defines a variable in a statistical study?

The complete group of individuals being studied
A numerical summary calculated from all collected data
A single person or object included in the study
A characteristic of an individual that is measured or observed

A characteristic of an individual that is measured or observed

Explication

A variable is a characteristic of an individual that is measured or observed. The individual is the person or object, while the variable is the characteristic recorded about it.

7. Which variable is quantitative rather than qualitative?

The preferred music category of a person
The nationality of a person
The gender of a person
The age of a person

The age of a person

Explication

Age is quantitative because it has numerical values for which operations such as averaging make sense. Nationality, gender, and music category place individuals into qualitative groups.

8. What does a population parameter describe?

A conclusion drawn from sample data
A numerical aspect of a population
A visual display of sample data
A numerical aspect of a sample

A numerical aspect of a population

Explication

A population parameter is a numerical measure describing an aspect of an entire population. A measure describing a sample is a sample statistic.

9. Which statement correctly distinguishes a sample statistic from a population parameter?

Both describe populations, but only parameters can be numerical
A sample statistic describes a population, whereas a population parameter describes a sample
A sample statistic describes a sample, whereas a population parameter describes a population
Both describe samples, but only statistics can vary

A sample statistic describes a sample, whereas a population parameter describes a population

Explication

A sample statistic summarizes a sample, while a population parameter summarizes the full population. Confusing these two scopes reverses their definitions.

10. A researcher repeatedly selects different samples from the same population. Which quantity is expected to remain fixed across these samples?

The sample statistic
The sample size
The sample composition
The population parameter

The population parameter

Explication

A parameter for a given population is fixed. Statistics calculated from different samples may vary from sample to sample.

11. Which type of measurement consists of categories with no implied order?

Nominal
Ordinal
Ratio
Interval

Nominal

Explication

Nominal measurement uses names, labels, or categories without an implied ranking. Unlike ordinal data, nominal categories cannot be arranged meaningfully from low to high.

12. A survey records customer ratings as poor, fair, good, and excellent. Which level of measurement is represented?

Nominal
Ordinal
Ratio
Interval

Ordinal

Explication

These ratings can be arranged in a meaningful order, but the differences between adjacent ratings are not known to be equal. That defines the ordinal level.

13. Which characteristic distinguishes interval measurement from ratio measurement?

Interval data have meaningful ratios and a true zero
Interval data have meaningful differences but lack a true zero
Interval data have categories with no meaningful order
Interval data cannot be arranged in an order

Interval data have meaningful differences but lack a true zero

Explication

Interval data are ordered and have meaningful differences, but zero is merely a position on the scale rather than a complete absence. Ratio data additionally have a true zero and meaningful ratios.

14. Which feature is essential to the ratio level of measurement?

An order without meaningful differences
A scale with meaningful differences but no true zero
A true zero and meaningful ratios
Categories without any ordering

A true zero and meaningful ratios

Explication

Ratio data have an order, meaningful differences, meaningful ratios, and a true zero. The true zero distinguishes ratio measurement from interval measurement.

15. Which activity is an example of descriptive statistics?

Predicting a population trend from sample results
Using a sample to estimate a population characteristic
Summarizing the observed scores in a dataset
Testing whether a population differs from a hypothesized value

Summarizing the observed scores in a dataset

Explication

Descriptive statistics organize, picture, and summarize information from samples or populations. Drawing conclusions about a broader population from a sample is inferential statistics.

16. A pollster uses responses from 1,000 sampled voters to estimate the preference of all eligible voters. What type of statistics is being used?

Descriptive statistics
Ordinal measurement
Inferential statistics
Nominal measurement

Inferential statistics

Explication

Inferential statistics uses information from a sample to draw conclusions about the population. Simply organizing or summarizing the 1,000 responses would be descriptive statistics.

17. Which statement best defines a simple random sample?

Individuals who are easiest to contact are selected until the sample size is reached
Individuals are selected at regular intervals after choosing a convenient starting point
Every individual and every sample of the specified size has an equal chance of selection
Individuals are selected from each subgroup in proportion to its population size

Every individual and every sample of the specified size has an equal chance of selection

Explication

In a simple random sample, every individual and every possible sample of the specified size has an equal chance of being selected. Selecting readily available individuals describes convenience sampling.

18. Which procedure correctly selects a simple random sample of 30 cars from a population of 500 cars?

Number the cars from 1 to 500 and use a random-number generator to choose 30 numbers
Divide the cars by type and choose all cars from one randomly selected type
Select every tenth car after choosing the first car that is easiest to identify
Choose the 30 cars parked closest to the researcher’s location

Number the cars from 1 to 500 and use a random-number generator to choose 30 numbers

Explication

A simple random sample can be drawn by numbering all 500 cars and using a random mechanism to select 30 corresponding numbers. The other procedures do not give every possible sample an equal chance of selection.

19. What is a simulation in the context of investigating real-world phenomena?

A survey that collects responses from every member of a population
A direct experiment that observes or manipulates the real situation itself
A sampling method that selects every kth member after a random start
A numerical representation or mathematical imitation of a real-world phenomenon

A numerical representation or mathematical imitation of a real-world phenomenon

Explication

A simulation numerically represents or mathematically imitates a real-world phenomenon and can be useful when direct investigation is dangerous. It differs from conducting an experiment in the actual situation.

20. A researcher divides a population into age groups and randomly selects individuals from every group. Which sampling design is being used?

Stratified sampling
Systematic sampling
Cluster sampling
Multistage sampling

Stratified sampling

Explication

Stratified sampling divides the population into characteristic-based strata and randomly samples from each stratum. Cluster sampling instead selects pre-existing clusters and includes every member of selected clusters.

21. Which sampling design selects every kth population member after choosing a random starting point?

Cluster sampling
Stratified sampling
Systematic sampling
Multistage sampling

Systematic sampling

Explication

Systematic sampling begins with a randomly selected starting point and then selects every kth member. Multistage sampling uses several sampling methods to form progressively smaller groups whose final sample consists of clusters.

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What is Statistics?

The study of how to collect, organize, analyze, and interpret data.

What is the first step in a statistical investigation cycle?

Posing a question.

What step follows collecting data in a statistical investigation?

Analyzing the data.

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