Examples of inferential statistics in the following topics:

 Contrast descriptive and inferential statistics
Descriptive statistics and inferential statistics are both important components of statistics when learning about a population.
 Descriptive statistics are distinguished from inferential statistics in that descriptive statistics aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.
 Descriptive statistics are distinguished from inferential statistics in that descriptive statistics aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.
 This generally means that descriptive statistics, unlike inferential statistics, are not developed on the basis of probability theory.
 Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented.
 descriptive statistics (noun) A branch of mathematics dealing with summarization and description of collections of data sets, including the concepts of arithmetic mean, median, and mode.
 inferential statistics (noun) A branch of mathematics that involves drawing conclusions about a population based on sample data drawn from it.

 Discuss how inferential statistics allows us to draw conclusions about a population from a random sample and corresponding tests of significance.
 The mathematical procedure in which we make intelligent guesses about a population based on a sample is called inferential statistics.
 More substantially, the terms statistical inference, statistical induction, and inferential statistics are used to describe systems of procedures that can be used to draw conclusions from data sets arising from systems affected by random variation, such as observational errors, random sampling, or random experimentation.
 The mathematical procedures whereby we convert information about the sample into intelligent guesses about the population fall under the rubric of inferential statistics.
 Inferential statistics are based on the assumption that sampling is random.
 inferential statistics (noun) A branch of mathematics that involves drawing conclusions about a population based on sample data drawn from it.

 A critical part of inferential statistics involves determining how far sample statistics are likely to vary from each other and from the population parameter.
 The sampling distribution of a statistic is the distribution of that statistic, considered as a random variable, when derived from a random sample of size n.
 Inferential statistics involves generalizing from a sample to a population.
 A critical part of inferential statistics involves determining how far sample statistics are likely to vary from each other and from the population parameter.
 This statistic is then called the sample mean.
 inferential statistics (noun) A branch of mathematics that involves drawing conclusions about a population based on sample data drawn from it.
 sampling distribution (noun) The probability distribution of a given statistic based on a random sample.

 Learning Objectives
State the assumptions that inferential statistics in regression are based upon
Identify heteroscedasticity in a scatter plot
Compute the standard error of a slope
Test a slope for significance
Construct a confidence interval on a slope
Test a correlation for significance
Construct a confidence interval on a correlation
This section shows how to conduct significance tests and compute confidence intervals for the regression slope and Pearson's correlation.
 Although no assumptions were needed to determine the bestfitting straight line, assumptions are made in the calculation of inferential statistics.
 Recall the general formula for a t test:
$\displaystyle{t=\frac{\text{statistics}\text{hypothesized value}}{\text{estimated standard error of the statistic}}}$
As applied here, the statistic is the sample value of the slope (b) and the hypothesized value is 0.

 Learning Objectives
Define inferential statistics
Graph a probability distribution for the mean of a discrete variable
Describe a sampling distribution in terms of "all possible outcomes"
Describe a sampling distribution in terms of repeated sampling
Describe the role of sampling distributions in inferential statistics
Define the standard error of the mean
Suppose you randomly sampled 10 people from the population of women in Houston, Texas, between the ages of 21 and 35 years and computed the mean height of your sample.
 Recall that inferential statistics concern generalizing from a sample to a population.
 A critical part of inferential statistics involves determining how far sample statistics are likely to vary from each other and from the population parameter.
 As we stated in the beginning of this chapter, sampling distributions are important for inferential statistics.
 Keep in mind that all statistics have sampling distributions, not just the mean.

 This can be valuable both for making patterns in the data more interpretable and for helping to meet the assumptions of inferential statistics.

 A significance test for Pearson's r is described in the section inferential statistics for b and r.

 Is this an example of descriptive or inferential statistics?
 What would be the roles of descriptive and inferential statistics in the analysis of these data?

 Statistics is generally broken down into two categories: descriptive statistics and inferential statistics.
 However, much of statistics is also nonmathematical.
 In short, statistics is the study of data.
 It includes descriptive statistics (the study of methods and tools for collecting data, and mathematical models to describe and interpret data) and inferential statistics (the systems and techniques for making probabilitybased decisions and accurate predictions based on incomplete data).
 Statistics itself also provides tools for predicting and forecasting the use of data and statistical models.
 statistics (noun) a mathematical science concerned with data collection, presentation, analysis, and interpretation

 Statistics also provides tools for prediction and forecasting.
 This is called descriptive statistics .
 Statistical models can also be used to draw statistical inferences about the process or population under study—a practice called inferential statistics.
 Inferential statistics uses patterns in the sample data to draw inferences about the population represented, accounting for randomness.
 Probability is used in "mathematical statistics" (alternatively, "statistical theory") to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures.
 sample (noun) a subset of a population selected for measurement, observation, or questioning to provide statistical information about the population