Examples of inferential statistics in the following topics:

 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.
 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.
 The use of descriptive and summary statistics has an extensive history and, indeed, the simple tabulation of populations and of economic data was the first way the topic of statistics appeared.

 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.
 Discuss how inferential statistics allows us to draw conclusions about a population from a random sample and corresponding tests of significance.

 Although no assumptions were needed to determine the bestfitting straight line, assumptions are made in the calculation of inferential statistics.
 As applied here, the statistic is the sample value of the slope (b) and the hypothesized value is 0.

 Statistics also provides tools for prediction and forecasting.
 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.
 In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount as simply as possible.

 The sampling distribution of a statistic is the distribution of the statistic for all possible samples from the same population of a given size.
 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.
 It may be considered as the distribution of the statistic for all possible samples from the same population of a given size.
 The sampling distribution depends on: the underlying distribution of the population, the statistic being considered, the sampling procedure employed, and the sample size used.

 The standard deviation of the sampling distribution of a statistic is referred to as the standard error of that quantity.
 For the case where the statistic is the sample mean, and samples are uncorrelated, the standard error is:
 When designing statistical studies where cost is a factor, this may have a role in understanding costbenefit tradeoffs.
 A statistical study can be said to be biased when one outcome is systematically favored over another.
 Finally, the variability of a statistic is described by the spread of its sampling distribution.

 The science of statistics deals with the collection, analysis, interpretation, and presentation of data.We see and use data in our everyday lives.
 Statistical inference uses probability to determine how confident we can be that the conclusions are correct.
 The goal of statistics is not to perform numerous calculations using the formulas, but to gain an understanding of your data.
 If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life.

 Descriptive statistics are numbers that are used to summarize and describe data.
 Any other number we choose to compute also counts as a descriptive statistic for the data from which the statistic is computed.
 Generalizing from our data to another set of cases is the business of inferential statistics, which you'll be studying in another section.
 You probably know that descriptive statistics are central to the world of sports.
 There are many descriptive statistics that we can compute from the data in the table.

 Finally, we compute the estimate's standard error and apply our inferential framework.

 In this section we develop inferential methods for a single proportion that are appropriate when the sample size is too small to apply the normal model to ˆ p.