Question 1

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

Accepted Answer

In a normal distribution, the area under the curve beyond ±1.96 standard deviations (or standard errors, if the context is estimating a population parameter) from the mean encompasses approximately 5% of the total area (2.5% in each tail).

Question 2

A ______ allows the researcher to obtain measurements for all members of a population.
A) sample
B) census
C) parameter
D) distribution

Accepted Answer

A census is the collection of data from every member of a population, whereas a sample is only a selected group of individuals from the population. Parameters refer to numerical measures that describe characteristics of the population, and distribution is the pattern of variation in data.

Question 3

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

Accepted Answer

A population refers to the entire group of people we are interested in studying. A sample is a smaller subset of the population that we select to study. A random sample is a sample selected randomly from the population. A universe is not typically used in sampling terminology.

Question 4

The average amount given to a political candidate is an example of a ______.
A) sample statistic
B) population
C) sample
D) population parameter

Accepted Answer

The average amount given to a political candidate pertains to the entire population of people who have donated to the candidate. Therefore, it is a population parameter.

Question 5

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

Accepted Answer

Random sampling error occurs due to chance and is inherent in the process of sampling. It is not due to bias, sloppiness or poor research design.

Question 6

The US Census is an example of a ______.
A) sample
B) population
C) random sample
D) universe

Accepted Answer

The US Census is a complete count of the entire population, meaning it is an example of a population.

Question 7

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

Accepted Answer

Using the formula for converting Z scores to actual values:
Z = (X - mean) / standard deviation

We plug in the values given:
1.96 = (X - 70) / 1.5
1.96(1.5) = X - 70
2.94 = X - 70
X = 67.06

Therefore, John's height is 6'1 (since we are given the heights in feet and inches).

Question 8

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

Accepted Answer

A public opinion poll is a sample that reports a sample statistic (the president's job approval rating), not a population parameter (which would require examining the entire population).

Question 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

Accepted Answer

Random sampling error is the difference between a sample statistic and the true population parameter due to chance variation. Therefore, the level of random sampling error is directly related to the amount of variation in the population characteristic being measured. The more variation in the characteristic, the greater the potential for random sampling error.

Question 10

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

Accepted Answer

A sampling distribution shows how random sampling error shapes the expected values of sampling statistics. It allows researchers to estimate the likelihood of obtaining a certain outcome or statistic by chance alone, which is crucial in determining the significance of research findings. The standard deviation (B) is a measure of variability, the unit of analysis (C) refers to the level of analysis in a study (e.g. individual, group, organization), and a sampling frame (D) is the list of all members of the population that can be sampled.

Question 11

Researchers study small groups of units of analyses to learn about the characteristics of a ______.
A) sample
B) population
C) universe
D) census

Accepted Answer

Researchers study small groups (samples) to learn about the characteristics of a larger group (population). The term "population" refers to the entire group of individuals or instances about whom the research is concerned.

Question 12

In a normal distribution ______ percent of all scores fall with two standard deviations of the mean.
A) 99
B) 68
C) 50
D) 95

Accepted Answer

The empirical rule states that approximately 95% of all scores will fall within two standard deviations of the mean in a normal distribution.

Question 13

A Z score is a method used to ______ the scores in a normal distribution.
A) standardize
B) report
C) measure
D) manipulate

Accepted Answer

A Z score is used to standardize scores in a normal distribution by converting them to a standard score with a mean of 0 and a standard deviation of 1.

Question 14

In statistical notation, the symbol σ refers to the ______.
A) sample size
B) variance
C) error
D) standard deviation

Accepted Answer

The symbol σ specifically refers to the standard deviation, which is a measure of how much the data values in a sample or population vary from the mean.

Question 15

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

Accepted Answer

A sample is a subset of a population, and it is used to make inferences or conclusions about the population. A census, on the other hand, is an attempt to collect data on every member of a population. The terms "universe" and "population" are often used interchangeably, but a population technically refers to the group of individuals or objects that share a common characteristic and are of interest to the researcher.

Question 16

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

Accepted Answer

A Z score of 1.96 tells us how many standard deviations from the mean a sample mean is located in a normal distribution. Specifically, a Z score of 1.96 represents a sample mean that is 1.96 standard deviations above the population mean.

Question 17

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

Accepted Answer

The magnitude of random sampling error is affected by the size of the sample and the amount of variation in the population being studied. A larger sample size generally results in a smaller sampling error, while a greater amount of variation in the population characteristic being measured will increase the size of the sampling error. Therefore, choice B, size and variation, is the best answer.

Question 18

In statistical notation, the letter n refers to the ______.
A) standard deviation
B) variance
C) sample size
D) sampling error

Accepted Answer

"n" refers to the sample size in statistical notation.

Question 19

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

Accepted Answer

The interval within which 95 percent of all possible sample estimates will fall by chance is defined as the sample mean ±1.96 standard errors, also known as the 95% confidence interval. This means that if we repeatedly sample from the population and calculate the mean, 95% of the time we will find the true population mean within this interval. Choices A and B are not correct, as they refer to specific boundaries rather than the range of all possible estimates. The central limit theorem is a mathematical concept that explains why the distribution of sample means tends to be normal, but it does not directly relate to confidence intervals.

Question 20

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

Accepted Answer

Quadrupling the sample size reduces the standard error (and thus the magnitude of random sampling error) by half, because the standard error of the mean is inversely proportional to the square root of the sample size.

Quiz 6: Foundations of Statistical Inference

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

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

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 ______.

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

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

The US Census is an example of a ______.

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

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

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

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

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

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

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

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

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

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.

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

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

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