Chapter 7 Questions

What is a sampling distribution of a sample and what can it be used for?

A sampling distribution of a sample statistic is a theoretical expression that describes the mean, variation, and shape of the distribution of an infinite number of occurrences of the statistic when calculated on samples of size N drawn independently and randomly from a population. It can be used as a statistical tool for calculating the probability that sample statistics fall within certain distances of the population parameter. The sample information cannot, of course, tell us exactly where within the range of values the population parameter lies. But it allows us to make an educated guess.

Characteristics of populations, such as averages, differences between groups, and relationships among variables that can be quantified as a number are called _______________.

(Population) parameters

What are the advantages and disadvantages of using a sample instead of a population and vice versa?

A researcher's decision whether to collect data for a population or for a sample is usually made on practical grounds. If time, money, and other costs were not considerations, it would almost always be better to collect data for a population, because we would then be sure that the observed cases accurately reflected the population characteristics of interest. However, in many if not most instances it is simply not possible or feasible to study an entire population. Imagine, for instance, the difficulty of attempting to interview every adult in even a small city. Since research is costly and time consuming, researchers must weigh the advantages and disadvantages of using a population or a sample. The advantages of taking a sample are often savings in time and money. The disadvantage is that information based on a sample is usually less accurate or more subject to error than is information collected from a population.

A(n) _____________ is a sample statistic based on sample observations that estimates the numerical value of a population characteristic, or parameter.

Estimator

The mean of many independently and randomly chosen samples, their average or mean will equal the corresponding true, or population, quantity, no matter what the sample size is called the

Expected Value

How do we determine the expected value of a population parameter?

If statistics are calculated for each of many independently and randomly chosen samples, their average or mean will equal the corresponding true, or population, quantity, no matter what the sample size.

The major goal of statistical inference is to make supportable conjectures about the unknown characteristics of a

Population

A _______________ sample is simply a sample for which each element in the total population has a known probability of being included in the sample.

Probability

A(n) ___________ is any subset of units collected in some manner from a population.

Sample

If a sampling frame is incomplete or inappropriate, ___________ will occur.

Sample bias

__________________ are used to approximate the corresponding population values, or parameters.

Sample statistics

A(n) _____________ is the discrepancy between an observed and a true value that arises because only a portion of a population is observed.

Sampling error

The particular population from which a sample is actually drawn is called a _____________.

Sampling frame

A ___________ is an entity listed in a sampling frame

Sampling unit

In a __________ sample, respondents are used to identify other persons who might qualify for inclusion in the sample.

Snowball

The mathematical term for the variation around the expected value is the _____________.

Standard error of the estimator, or standard error

A __________ sample is a probability sample in which elements sharing one or more characteristics are grouped, and elements are selected from each group in proportion to the group's representation in the total population.

Stratified

A ___________ sample in which elements are selected from a list at predetermined intervals.

Systematic

Systematic sampling is a probability sampling method and therefore takes advantage of random assignment to avoid bias. In your answer, please identify and explain one scenario under which a systematic sampling technique would result in a biased sample.

The answer to this question will vary with the student's example, but should follow the following line of argument. Systematic sampling may result in a biased sample in at least two situations. One occurs if elements on the list have been ranked according to a characteristic. In that situation the position of the random start will affect the average value of the characteristic for the sample. For example, if students were ranked from the lowest to the highest GPA, a systematic sample with students 1, 51, and 101 would have a lower GPA than a sample with students 50, 100, and 150. Each sample would yield a GPA that presented a biased picture of the student population.

Please explain the logic behind statistical inference.

The goal of statistical inference is to make supportable conjectures about the unknown characteristics of a population based on sample statistics. Statistical inference refers to using the information we know about a sample to make assertions about the information we do not know about a population.

Please define three random and three nonrandom sampling techniques.

This question can be as narrow or broad as the instructor wants by changing the number of techniques to be included in the question.

A ________ sample is a probability sample in which the sampling frame initially consists of groups of elements.

Cluster

A(n) ____________ is a single occurrence, realization, or instance of the objects or entities being studied.

Element, or unit of analysis is also acceptable

What is a disproportionate stratified sample and why would you use one? In your answer, please include an example.

If we wished to analyze a population as a whole, a simple random sample might be an acceptable sample. But if we wished to investigate a question by looking at a small stratum within a large population using a simple random sample, we would find that the number of observations from the stratum of interest is too small a sample with which to draw inferences. To get around this problem we could use a disproportionate stratified sample—by including a far larger proportion of observations from the stratum of interest than is found in the population. Then we would have enough observations to draw inferences about the population of interest. For example, suppose we are conducting a survey of 200 students at a college in which there are 500 liberal arts majors, 100 engineering majors, and 200 business majors, for a total of 800 students and we wished to investigate students in each major separately, we would find that 25 engineering students was too small a sample with which to draw inferences about the population of engineering students. To get around this problem we could sample disproportionately—for example, we could include 100 liberal arts majors, 50 engineering majors, and 50 business majors in our study. Then we would have enough engineering students to draw inferences about the population of engineering majors. The problem now becomes evaluating the student population as a whole, since our sample is biased due to an undersampling of liberal arts majors and an oversampling of engineering majors. Suppose engineering students have high GPAs. Our sample estimate of the student body's GPA would be biased upward because we have oversampled engineering students. Therefore, when we wish to analyze the total sample, not just a major, we need some method of adjusting our sample so that each major is represented in proportion to its real representation in the total student population.

A ____________ sample is one in which each element in the population has an unknown probability of being selected.

Nonprobability