Question 1

Social scientists study many different populations, but what is a major complication they often face?
A) Populations are often too large to study.
B) Populations are often not representative.
C) Samples are often too large to study.
D) Sampling distributions are often not random.

Accepted Answer

A

Question 2

Which of the following is a common reason that researchers often use samples to test a theory?
A) Populations are often not representative of all the relevant cases needed to test a theory.
B) Actual data can be gathered only from samples; populations are merely theoretical.
C) It is often not feasible to collect data from every case in the population.
D) Populations are often too small to accurately test a theory.

Accepted Answer

It is often not feasible to collect data from every case in the population due to constraints like time, cost, and accessibility, so researchers use samples to make inferences about the population.

Question 3

The average age for a population of doctors in a hospital is 51.6 years. What does this mean value represent?
A) a statistic
B) a parameter
C) a sample
D) a standard error

Accepted Answer

The average age of 51.6 years represents a parameter because it describes a characteristic of the entire population of doctors in the hospital.

Question 4

A researcher finds that 4% of people in a convenience sample of university students are smokers. What can she conclude about other young people who attend other universities in the same city?
A) They are unlikely to smoke.
B) Between 2% and 10% of them are likely to smoke.
C) They are very likely to smoke.
D) She can conclude nothing.

Accepted Answer

The researcher cannot generalize the findings from a convenience sample of one university to other universities, as the sample may not be representative.

Question 5

Which of these research scenarios would be appropriate for using a nonprobability sample?
A) to determine whether Canadian prisoners are less healthy than the rest of the population
B) to explore whether research subjects understood the wording for a newly developed survey question before it was included on a nationwide survey
C) to compare the prevalence of asthma in Canada with the prevalence in India
D) There is never an appropriate situation for using nonprobability samples.

Accepted Answer

Nonprobability sampling is suitable for exploratory research, such as testing survey questions, where the goal is not to generalize findings to the entire population but to gain insights or improve the survey design.

Question 6

What does it mean for a sample to be representative?
A) The sample is very large.
B) The sample has a low probability of being random.
C) The sample reproduces the important characteristics of the population.
D) The sample has no standard error.

Accepted Answer

A representative sample accurately reflects the characteristics of the population from which it is drawn, ensuring that conclusions drawn from the sample can be generalized to the population.

Question 7

Which of the following is a required characteristic of a sample if it is to be used to make accurate generalizations to a population?
A) The sample must be very large.
B) The sample must be representative.
C) The sample must be nonprobability.
D) The sample must be stratified.

Accepted Answer

A representative sample accurately reflects the characteristics of the population from which it is drawn, allowing for valid generalizations.

Question 8

Which of the following is a limitation of simple random sampling?
A) It uses non-random samples.
B) It violates the rule of EPSEM.
C) It does not guarantee representativeness.
D) It does not use representative samples.

Accepted Answer

Simple random sampling does not guarantee representativeness because, by chance, the selected sample may not reflect the diversity or characteristics of the entire population.

Question 9

Which of the following is the best example of an EPSEM sample?
A) assigning the students of mid-size introductory biology class random numbers, arranging the numbers in order, then selecting every fifth student
B) identifying every house located on a street corner within Ottawa's city limits and selecting all homes on the south-eastern quadrant of the street corners
C) selecting the three largest cities from a Canadian province and inviting each resident to join a research project
D) standing on the street corner and asking every other passerby to participate in a survey study

Accepted Answer

Assigning random numbers and selecting every fifth student ensures that each student has an equal probability of being selected, which is characteristic of an EPSEM (Equal Probability of Selection Method) sample.

Question 10

Which of these pairs describes things a researcher needs in order to select a simple random sample?
A) a parameter and a distribution
B) a sampling distribution and a table of random numbers
C) a list of the sample, and a well-developed sampling distribution
D) a list of the population, and a system for selecting cases according to EPSEM

Accepted Answer

A researcher needs a list of the population and a system for selecting cases according to EPSEM (Equal Probability of Selection Method) to ensure each member of the population has an equal chance of being selected in a simple random sample.

Question 11

Which is the most basic EPSEM sampling technique?
A) a convenience sample
B) a simple random sample
C) a systematic sample
D) a stratified sample

Accepted Answer

A simple random sample is the most basic EPSEM (Equal Probability of Selection Method) sampling technique, where each member of the population has an equal chance of being selected.

Question 12

Suppose we wish to study Canadian newspaper content published in the Globe and Mail from 1980 to the present, and we deem a sample of 50 articles to be adequate for our research purposes. Which of the following would best represent the sampling distribution relevant for our research project?
A) a single sample that fulfilled the EPSEM requirements
B) 50 samples of size 50 drawn from the full archive of articles published from 1980 to the present
C) 50 × 50 = 2,500 samples of size 50 drawn from the full archive of articles published from 1980 to the present
D) every possible combination of 50 articles from the full archive of articles published from 1980 to the present

Accepted Answer

The sampling distribution is best represented by every possible combination of 50 articles from the full archive, as it considers all potential samples of that size.

Question 13

A researcher gathers a random sample of 110 Canadian adults. Which sample value could NOT be observed in the sampling distribution of sample means if the mean income of Canadians is $58,355?
A) mean income $9,440
B) mean income $40,000
C) mean income $330,00
D) No sample means are impossible to observe in the sampling distribution.

Accepted Answer

The sampling distribution of sample means is a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, all possible sample means are possible to observe in the sampling distribution.

Question 14

The mean age of Canadian MPs is 52.7 years. What is the mean of the sampling distribution, assuming a normal distribution of age in the population?
A) within 1 standard error of 52.7
B) within 2 standard errors of 52.7
C) within 3 standard errors of 52.7
D) 52.7

Accepted Answer

The mean of the sampling distribution of the sample mean is equal to the population mean, which is 52.7 years.

Question 15

Which set of symbols represents the standard deviation of the sampling distribution?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Which set of symbols represents the standard...

Question 16

What type of shape do histograms of sampling distributions based on large samples have?
A) bell-shaped and symmetrical
B) evenly-distributed (i.e., no discernible modal point)
C) highly skewed
D) The shape differs depending on the variable.

Accepted Answer

Histograms of sampling distributions based on large samples tend to be bell-shaped and symmetrical due to the Central Limit Theorem, which states that the distribution of sample means will approximate a normal distribution as the sample size becomes large, regardless of the shape of the population distribution.

Question 17

When is the sampling distribution of sample means normal?
A) whenever the variable is normal in the population, regardless of sample size
B) whenever the sample is skewed, but only if the sample size is greater than n =10
C) whenever the mean is equal to the standard deviation but sample size is less than n =50
D) The shape of the sampling distribution can never be known.

Accepted Answer

The sampling distribution of sample means is normal if the population distribution is normal, regardless of the sample size, due to the Central Limit Theorem.

Question 18

Which of these terms is synonymous with the standard error of the mean?
A) the variance of a sample
B) the standard deviation of a sample
C) the standard deviation of a population
D) the standard deviation of a sampling distribution

Accepted Answer

The standard error of the mean is the standard deviation of the sampling distribution of the sample mean.

Question 19

Business researchers wish to estimate the mean quarterly earnings from a population of 600 companies. If the true population mean is 6.2 million dollars, which of the following sample sizes would be most likely to produce a sample mean statistic within $2,000 of the population mean parameter?
A) sample size 10
B) sample size 50
C) sample size 160
D) Each of the samples will be equally likely to produce a sample statistic within $2,000 of the population parameter.

Accepted Answer

A larger sample size generally results in a sample mean that is closer to the population mean due to the law of large numbers, reducing the margin of error.

Question 20

Which of these statements refers to the mean of a sampling distribution of sample means?
A) the same as the population mean
B) representative of the entire population
C) close to the value of the sample mean
D) between the population and sample means in value

Accepted Answer

The mean of a sampling distribution of sample means, also known as the expected value of the sample mean, is equal to the population mean according to the Central Limit Theorem.

Quiz 5: Introduction to Inferential Statistics: Sampling and the Sampling Distribution

Social scientists study many different populations, but what is a major complication they often face?

Which of the following is a common reason that researchers often use samples to test a theory?

The average age for a population of doctors in a hospital is 51.6 years. What does this mean value represent?

A researcher finds that 4% of people in a convenience sample of university students are smokers. What can she conclude about other young people who attend other universities in the same city?

Which of these research scenarios would be appropriate for using a nonprobability sample?

What does it mean for a sample to be representative?

Which of the following is a required characteristic of a sample if it is to be used to make accurate generalizations to a population?

Which of the following is a limitation of simple random sampling?

Which of the following is the best example of an EPSEM sample?

Which of these pairs describes things a researcher needs in order to select a simple random sample?

Which is the most basic EPSEM sampling technique?

Suppose we wish to study Canadian newspaper content published in the Globe and Mail from 1980 to the present, and we deem a sample of 50 articles to be adequate for our research purposes. Which of the following would best represent the sampling distribution relevant for our research project?

A researcher gathers a random sample of 110 Canadian adults. Which sample value could NOT be observed in the sampling distribution of sample means if the mean income of Canadians is $58,355?

The mean age of Canadian MPs is 52.7 years. What is the mean of the sampling distribution, assuming a normal distribution of age in the population?

Which set of symbols represents the standard deviation of the sampling distribution?

What type of shape do histograms of sampling distributions based on large samples have?

When is the sampling distribution of sample means normal?

Which of these terms is synonymous with the standard error of the mean?

Business researchers wish to estimate the mean quarterly earnings from a population of 600 companies. If the true population mean is 6.2 million dollars, which of the following sample sizes would be most likely to produce a sample mean statistic within $2,000 of the population mean parameter?

Which of these statements refers to the mean of a sampling distribution of sample means?