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

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.

Answer 1

Populations are often too large to study.

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.

Answer 2

It is often not feasible to collect data from every case in 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

Answer 3

a parameter

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.

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.

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.

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.

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.

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

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

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

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

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.

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

Question 15

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

A)
B)
C)
D)

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.

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.

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

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.

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

Question 21

According to the Central Limit Theorem, which of the following sampling distributions will be normal?

A) a sampling distribution derived from a sample of 25 abandoned dogs drawn randomly from a dog shelter
B) a sampling distribution derived from a non-random sample of 500 Canadian adults for a variable that is nearly normal in the population
C) a sampling distribution derived from a random sample of 135 villages in Thailand
D) The Central Limit Theorem makes no claims about the shape of the sampling distribution, only about the sample's distribution.

Question 22

Researchers drew a random sample of 5,000 Scottish school teachers. Which of these variables' sampling distributions are unlikely to be normal?

A) years worked
B) pension savings
C) number of siblings
D) Assuming the sample is random, no sampling distribution is unlikely to be normal.

Question 23

Which of the following is an assurance that the sampling distribution is normal?

A) The sample is large.
B) The sample is normal.
C) The sample is random.
D) The population is small.

Question 24

A researcher's sample size is 1,000. Which of the following is it safe for the researcher to assume?

A) The population distribution is normal.
B) The shape of the sampling distribution of sample means is normal.
C) The sample is representative of the population.
D) The sample distribution is normal.

Question 25

A prison has 140 prisoners. The mean number of prior convictions for this population is 4.6. If we drew a random sample of size 30, what would we calculate as the mean of the sampling distribution?

A)
B)
C)
D) 4.6

Question 26

Which of these statements will be the result when a sampling distribution is compared to a population distribution?

A) The two distributions will always be the same.
B) The two distributions will become identical as the size of the sample increases.
C) There will always be more variance in the population distribution.
D) There will always be more variance in the sampling distribution.

Question 27

The average number of monthly sales made by employees of an insurance company is 13.5. The standard deviation is 4. What would be the standard error for a sample of size 64?

A) 0.25
B) 0.50
C) 1
D) 3.38

Question 28

In most practical research scenarios, which of the following pieces of information would a researcher be most able to provide?

A) the standard deviation for the population
B) the mean of the sampling distribution
C) the mean of the sample
D) the standard error

Question 29

Explain the concept of a sampling distribution and why it is used for statistical inference.

Question 30

Explain the purpose of inferential statistics. Include in your answer the concepts and definitions of sample, population, statistic, parameter, representativeness, and the principle of EPSEM.

Question 31

Explain and briefly discuss simple random sampling. How is this technique designed to maximize representativeness?

Question 32

Define and distinguish between the sample distribution, the sampling distribution, and the population distribution. How are these three distributions related to each other in inferential statistics? What symbols are used to identify the means and standard deviations of each of the three distributions?

Question 33

A political scientist wanted to know about the political preferences of people in a large Canadian city. She obtained a random sample of size 500 using the list of all households in the city. After interviewing these 500 individuals, she found that 235 of 500 supported the NDP, 165 supported the Liberals, 80 supported the Progressive Conservatives, and 20 did not support any party.
Identify each of the following elements in this research scenario
a. Population
b. Sample
c. Parameter
d. Statistic

Question 34

A calculus instructor wished to understand whether students in her 180-person class enjoyed her lecture style. She decided to conduct an interview of 25 students to gain some insight into this question. She wanted to ensure that her sample followed the principles of EPSEM. Describe how she might obtain an EPSEM sample, and explain whether or not this sample would be representative of the class.