Chapter 7 Data for Decisions

Population vs Sample A Population in a statistical study is the entire group of individuals about which we want information. A Sample is part of the population from which we actually collect information used to draw conclusions about the whole.

Sampling Convenience Sampling is when you select the members of the population that are easiest to reach. This often produces unrepresentative data. A sample of mall shoppers is an example of convenience sampling. Why would this means of sampling not represent the population?

The design of a statistical study is biased if it systematically favors certain outcomes. A Voluntary Response Sample consists of people who choose themselves by responding to a general appeal. Voluntary response samples are biased because people with strong opinions are most likely to respond.

A Simple Random Sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected. Undercoverage occurs when some groups in the population are left out of the process of choosing the sample. Nonresponse occurs when an individual chosen for the sample can’t be contacted or refuses to participate.

Experiments An Observational study, such as a sample survey, observes individuals and measures variables of interest but does not attempt to influence the responses. The purpose of an observational study is to describe some group or situation. An Experiment, on the other hand, deliberately imposes some treatment on individuals in order to observe their responses. The purpose of an experiment is to study whether the treatment causes a change in the response.

Variables, whether part of a study or not, are said to be confounded when their effects on the outcome cannot be distinguished from each other. An observed effect so large that it would rarely occur by chance is called statistically significant.

Parameters vs Statistics A Parameter is a number that describes the Population. A parameter is a fixed number, but in practice we do not know its value. A Statistic is a number that describes a sample. The value of a statistic is known when we have taken a sample, but it can change from sample to sample. We often us a statistic to estimate an unknown parameter.

Sampling Distribution A Sampling Distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population. Shape: For large sample sizes, the sampling distribution of is approximately normal. Center: The mean of the sampling distribution is p. Spread: The standard deviation of the sampling distribution is

Confidence Interval A 95% confidence interval is an interval obtained from the sample data by a method that 95% of all samples will produce an interval containing the true population parameter. Choose a SRS of size n from a large population that contains an unknown proportion p of successes. A 95% confidence interval for p is