Statistics A Tool For Social Researchers in Canada 4Th Ed by Steven Prus – Test Bank


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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.




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.




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




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.




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.




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.




7. When do social scientists use inferential statistics to generalize to populations?

  a. after collecting a representative sample
  b. after collecting at least 100 cases from all possible populations
  c. after collecting an EPSEM sample from the population of interest
  d. after collecting all the information possible from the entire population




8. 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.




9. 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.




10. 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




11. 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




12. 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




13. 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




14. 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.




15. 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




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

  a. b.
  c. d.




17. 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.




18. Which of these statements is an assurance that the sampling distribution is normal?

  a. The sample is stratified. b. The population is small.
  c. The sample is normal. d. The population is normal.




19. Which of these phrases explains when a normal sampling distribution can be assumed if the sample size is 75?

  a. if the population distribution is normal
  b. if the cases in the sample are heterogeneous
  c. if the sample distribution is normal
  d. if the cases in the sample are homogeneous




20. 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 =10
  c. whenever the mean is equal to the standard deviation but sample size is less than =50
  d. The shape of the sampling distribution can never be known.




21. 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




22. 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.




23. 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




24. 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.




25. 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.




26. 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.




27. 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.




28. 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




29. 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.




30. 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




31. 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




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

ANSWER:   ∙ It is a theoretical entity: the distribution of a statistic (e.g., mean or proportion) for all possible sample outcomes of a certain size. In other words, if we were take every possible sample from a given population, the distribution of sample statistics would take the shape of the sampling distribution.
∙ If a random sample is taken, researchers can know how likely their sample is to reflect the larger population because the sampling distribution has known probability characteristics. Its shape, central tendency, and dispersion can be deduced.
∙ The population distribution is unknown, so we need the theoretical tool of the sampling distribution to make inferences from the observed sample to the unobserved population.


33. 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.

ANSWER:   Inferential statistics allow us to learn about large groups (populations) from small, carefully selected subgroups (samples). Such samples are selected using the principle of EPSEM, or the Equal Probability of Selection Method, which maximizes the chances that a sample is representative of the population from which it was drawn. The goal of inferential statistics is to learn about the characteristics of a population (called parameters) based on what we can learn from the characteristics of our samples (called statistics). A key concept in inferential statistics is the sampling distribution, which is the theoretical, probabilistic distribution of a statistic for all possible samples of a certain sample size (n). We link information from the sample to the population via the sampling distribution.


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

ANSWER:   The most basic EPSEM sampling technique produces a simple random sample. To draw a simple random sample, we need a list of all elements or cases in the population and a system for selecting cases from the list that will guarantee that every case has an equal chance of being selected for the sample. The selection process could be based on a number of different kinds of operations (e.g., drawing numbers from a hat), although cases are often selected by using tables of random numbers. Simple random sampling maximizes representativeness since every case in the population has an equal probability of being selected into the sample.


35. 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?

ANSWER:   The sample distribution is empirical (i.e., it exists in reality) and known. For example, we can ascertain the shape, central tendency, and dispersion of any variable from the sample. The population distribution, while empirical, is unknown (we do not collect data on every case in the population). The sampling distribution is non-empirical (i.e., theoretical). Because of the laws of probability, however, we know a great deal about this distribution, namely its shape, central tendency, and dispersion. Knowing that the sampling distribution of, for example, sample means is normal in shape with a mean equal to the population mean () and a standard deviation ( equal to the population standard deviation divided by the square root of n ( allows us to link the sample to the population.


36. 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

ANSWER:   a. Population: all people living in the city
b. Sample: 500 people from the city who were interviewed
c. Parameter: percent of all people in the city who support the NDP, the Liberals, the Progressive Conservatives, or some other party
d. Statistic: percent of people in the sample who support the NDP, the Liberals, the Progressive Conservatives, or some other party


37. 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.

ANSWER:   The simplest way for the teacher to follow EPSEM sampling techniques would be to obtain a random sample. She would need a list of all students in her class, and then use a method to make sure that every case has an equal chance of being selected for the sample (e.g., a random number generator). Each case in the population list would have to have an identification number, then the cases would be selected for the sample as they came up from random numbers. Using an EPSEM technique does not necessarily guarantee that the sample will be representative of the population, but it provides the highest probability that the sample will capture the characteristics of the class.



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