Statistics, Chapter 1 (Section 1.1)

Objective:

1. Construct a simple random sample 2. Determine when samples of convenience are acceptable 3. Describe stratified sampling, cluster sampling, systematic sampling, and voluntary response sampling 4. Distinguish between statistics and parameters

Sample

is a subset of a population, containing the individuals that are actually observed.

Simple Random Sample

of size n is a sample chosen by a method in which each collection of n population items is equally likely to make up the sample, just as in a lottery.

Systematic sampling

Imagine walking alongside a line of people and choosing every third one. That would produce a systematic sample. In a systematic sample, the population items are ordered. It is decided how frequently to sample items; for example, one could sample every third item, or every fifth item, or every hundredth item. Let k represent the sampling frequency. To begin the sampling, choose a starting place at random. Select the item in the starting place, along with every kth item after that.

Cluster sampling

In cluster sampling, items are drawn from the population in groups, or clusters. Cluster sampling is useful when the population is too large and spread out for simple random sampling to be feasible. Cluster sampling is used extensively by U.S. government agencies in sampling the U.S. population to measure sociological factors such as income and unemployment.

Stratified sampling

In stratified sampling, the population is divided into groups, called strata, where the members of each stratum are similar in some way. Then a simple random sample is drawn from each stratum. Stratified sampling is useful when the strata differ from one another, but the individuals within a stratum tend to be alike.

Sample of Convenience

Is a sample that is not drawn by a well-defined ransom method. • If it is reasonable to believe that no important systematic difference exists, then it is acceptable to treat the sample of convenience as if it were a simple random sample. subjects included in an investigation that appear to be selected merely because that are available, whether of not they are of optimal suitability to test the hypothesis

Voluntary response sampling

Voluntary response samples are often used by the media to try to engage the audience. For example, a news commentator will invite people to tweet an opinion, or a radio announcer will invite people to call the station to say what they think. How reliable are voluntary response samples? To put it simply, voluntary response samples are never reliable. People who go to the trouble to volunteer an opinion tend to have stronger opinions than is typical of the population. In addition, people with negative opinions are often more likely to volunteer their responses than those with positive opinions.

Parameter

A parameter is a number that describes a population. Now imagine that the election takes place, and that one of the items on the ballot is a proposition to raise the sales tax to pay for the development of a new park downtown. Let's say that 53% of the voters vote in favor of the proposition. The quantity "53%" describes the population of voters who voted in the election. A number that describes a population is called a parameter.

Statistic

A statistic is a number that describes a sample. We often use numbers to describe, or summarize, a sample or a population. For example, suppose that a pollster draws a sample of 500 likely voters in an upcoming election, and 68% of them say that the state of the economy is the most important issue for them. The quantity "68%" describes the sample. A number that describes a sample is called a statistic.