Chapter 6: Foundations of Statistical Inference

Test Bank

Multiple Choice

1. A large group of people of particular interest that we desire to study and understand, such as the people in a city or persons with jobs, is called a ______.

A. population

B. random sample

C. sample

D. universe

Learning Objective: 6-1: Why random sampling is of cardinal importance in political research.

Cognitive Domain: Comprehension

Answer Location: Population Parameters and Sample Statistics

Difficulty Level: Easy

2. The US Census is an example of a ______.

A. sample

B. population

C. random sample

D. universe

Learning Objective: 6-1: Why random sampling is of cardinal importance in political research.

Cognitive Domain: Application

Answer Location: Population Parameters and Sample Statistics

Difficulty Level: Medium

3. A particular number of cases drawn from the entire group a researcher wishes to study is known as a ______.

A. population

B. universe

C. sample

D. census

Learning Objective: 6-1: Why random sampling is of cardinal importance in political research.

Cognitive Domain: Comprehension

Answer Location: Population Parameters and Sample Statistics

Difficulty Level: Easy

4. The average amount given to a political candidate is an example of a ______.

A. sample statistic

B. population

C. sample

D. population parameter

Learning Objective: 6-1: Why random sampling is of cardinal importance in political research.

Cognitive Domain: Application

Answer Location: Population Parameters and Sample Statistics

Difficulty Level: Medium

5. A public opinion poll reporting the president’s job approval rating is an example of a ______.

A. sample statistic

B. population parameter

C. sample

D. census

Learning Objective: 6-1: Why random sampling is of cardinal importance in political research.

Cognitive Domain: Application

Answer Location: Population Parameters and Sample Statistics

Difficulty Level: Medium

6. Researchers study small groups of units of analyses to learn about the characteristics of a ______.

A. sample

B. population

C. universe

D. census

Learning Objective: 6-1: Why random sampling is of cardinal importance in political research.

Cognitive Domain: Comprehension

Answer Location: Population Parameters and Sample Statistics

Difficulty Level: Easy

7. Random sampling error is defined as the extent to which a sample statistic differs from a population parameter by ______.

A. chance

B. bias

C. sloppiness

D. poor research design

Learning Objective: 6-1: Why random sampling is of cardinal importance in political research.

Cognitive Domain: Comprehension

Answer Location: Population Parameters and Sample Statistics

Difficulty Level: Easy

8. The magnitude of random sampling error in a study depends upon the ______ of a sample and the amount of ______ in the population characteristic being measured.

A. error; bias

B. size; variation

C. variation; error

D. bias; variation

Learning Objective: 6-2: Why samples that seem small can yield accurate information about much larger groups.

Cognitive Domain: Comprehension

Answer Location: Quantifying Standard Errors

Difficulty Level: Medium

9. The level of random sampling error in a study is directly related to the ______ in the population characteristic.

A. people

B. ambiguity

C. variation

D. bias

Learning Objective: 6-2: Why samples that seem small can yield accurate information about much larger groups.

Cognitive Domain: Knowledge

Answer Location: Quantifying Standard Error

Difficulty Level: Easy

10. A researcher who wants to reduce the magnitude of random sampling error in her study by half should ______.

A. double the sample size

B. triple the sample size

C. quadruple the sample size

D. there is nothing she can do to reduce random sampling error

Learning Objective: 6-2: Why samples that seem small can yield accurate information about much larger groups.

Cognitive Domain: Knowledge

Answer Location: Quantifying Standard Error

Difficulty Level: Easy

11. In statistical notation, the letter n refers to the ______.

A. standard deviation

B. variance

C. sample size

D. sampling error

Learning Objective: 6-2: Why samples that seem small can yield accurate information about much larger groups.

Cognitive Domain: Knowledge

Answer Location: Quantifying Standard Error

Difficulty Level: Easy

12. In statistical notation, the symbol σ refers to the ______.

A. sample size

B. variance

C. error

D. standard deviation

Learning Objective: 6-2: Why samples that seem small can yield accurate information about much larger groups.

Cognitive Domain: Knowledge

Answer Location: Quantifying Standard Error

Difficulty Level: Easy

13. In a normal distribution, a Z score of 1.96 tells us what?

A. the sample size

B. the variance

C. how many standard deviations from the mean a sample mean is located

D. we need to increase our sample size

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Comprehension

Answer Location: Summary

Difficulty Level: Easy

14. In a normal distribution ______ percent of all scores fall with two standard deviations of the mean.

A. 99

B. 68

C. 50

D. 95

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Comprehension

Answer Location: The Central Limit Theorem and the Normal Distribution

Difficulty Level: Easy

15. A Z score is a method used to ______ the scores in a normal distribution.

A. standardize

B. report

C. measure

D. manipulate

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Knowledge

Answer Location: The Central Limit Theorem and the Normal Distribution

Difficulty Level: Easy

16. A researcher studying the height of college freshmen determines the average height of males to be 5’10 with a standard deviation of 1.5 inches. John has a Z score of +1.96, which means John is what height?

A. 5’7

B. 6’1

C. 6’4

D. 5’4

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Application

Answer Location: The Central Limit Theorem and the Normal Distribution

Difficulty Level: Hard

17. The interval within which 95 percent of all possible sample estimates will fall by chance is defined as ______.

A. lower confidence boundary

B. upper confidence boundary

C. the sample mean ±1.96 standard errors

D. the central limit theorem

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Comprehension

Answer Location: The Central Limit Theorem and the Normal Distribution

Difficulty Level: Medium

18. In a normal distribution the portion of the curve above 1.96 standard errors is ______.

A. 1 percent

B. 5 percent

C. 10 percent

D. 2.5 percent

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Knowledge

Answer Location: The Central Limit Theorem and the Normal Distribution

Difficulty Level: Easy

19. A ______ allows the researcher to obtain measurements for all members of a population.

A. sample

B. census

C. parameter

D. distribution

Learning Objective: 6-1: Why random sampling is of cardinal importance in political research.

Cognitive Domain: Knowledge

Answer Location: Population Parameters and Sample Statistics

Difficulty Level: Easy

20. A ______ shows how random sampling error shapes the expected values of sampling statistics.

A. sampling distribution

B. standard deviation

C. unit of analysis

D. sampling frame

Learning Objective: 6-1: Why random sampling is of cardinal importance in political research.

Cognitive Domain: Comprehension

Answer Location: Population Parameters and Sample Statistics

Difficulty Level: Easy

True/False

1. A researcher working with a sample size of 35 should use the Student’s t distribution to make inferences about the population mean.

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Comprehension

Answer Location: Inferences with Small Batches: The Student’s t-Distribution

Difficulty Level: Easy

2. The standard error of a sample mean is synonymous with random sampling error.

Learning Objective: 6-2: Why samples that seem small can yield accurate information about much larger groups.

Cognitive Domain: Knowledge

Answer Location: Standard Error of a Sample Mean

Difficulty Level: Easy

3. The idea that an infinite number of samples drawn from a population will have normally distributed means is called the central limit theorem.

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Comprehension

Answer Location: The Central Limit Theorem and the Normal Distribution

Difficulty Level: Easy

4. A normally distributed set of sample means resembles a standard bell curve.

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Comprehension

Answer Location: Inferences with Small Batches: The Student’s t-Distribution

Difficulty Level: Easy

5. Random sampling errors are mistakes or oversights made by the researchers.

Learning Objective: 6-1: Why random sampling is of cardinal importance in political research.

Cognitive Domain: Comprehension

Answer Location: Population Parameters and Sample Statistics

Difficulty Level: Easy

6. The standard error of a statistic is a single number.

Learning Objective: 6-1: Why random sampling is of cardinal importance in political research.

Cognitive Domain: Knowledge

Answer Location: Population Parameters and Sample Statistics

Difficulty Level: Easy

7. A standardized value is called a Z value or Z score.

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Knowledge

Answer Location: The Central Limit Theorem and the Normal Distribution

Difficulty Level: Easy

8. Variation in the population characteristic has a direct relationship with random sampling error: As variation goes up, random sampling error goes down.

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Comprehension

Answer Location: Quantifying Standard Errors

Difficulty Level: Easy

9. When a variable is measured at the nominal or ordinal-level, we don’t calculate its dispersion but say dispersion is maximized when observations are evenly divided among possible values.

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Comprehension

Answer Location: Quantifying Standard Errors

Difficulty Level: Easy

10. Many of the variables of interest to political researchers are not measured at the nominal level.

Learning Objective: 6-2: Why samples that seem small can yield accurate information about much larger groups.

Cognitive Domain: Comprehension

Answer Location: Standard Error of a Sample Proportion

Difficulty Level: Easy

11. A probability is defined as the likelihood of the occurrence of an event or set of events.

Ans. T

Learning Objective: 6-3: How to figure out the margin of error for the information in a sample

Cognitive Domain: Knowledge

Answer Location: Confidence Intervals

Difficulty Level: Easy

12. As consumers of popular media, we are more likely to encounter arithmetic means than percentages or proportions.

Learning Objective: 6-3: How to figure out the margin of error for the information in a sample

Cognitive Domain: Knowledge

Answer Location: Sample Size and the Margin of Error of a Poll

Difficulty Level: Easy

13. Degrees of freedom are a statistical property of a large family of distributions, including the Student’s t distribution.

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Knowledge

Answer Location: Inferences with Small Batches: The Student’s t-Distribution

Difficulty Level: Easy

14. The number of degrees of freedom is equal to the sample size, n, minus the number of parameters being estimated by the sample.

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Knowledge

Answer Location: Inferences with Small Batches: The Student’s t-Distribution

Difficulty Level: Easy

15. The larger the sample size, the lower the degrees of freedom, the more relaxed the t distribution.

Learning Objective: 6-4: How to use the normal curve to make inferences about the information in a sample.

Cognitive Domain: Comprehension

Answer Location: Inferences with Small Batches: The Student’s t-Distribution

Difficulty Level: Easy