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 conclusion of a statistical inference is a statistical proposition.

 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.

 State the assumptions that inferential statistics in regression are based upon
 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.
 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.

 With this example, you have begun your study of statistics.
 Organizing and summarizing data is called descriptive statistics.
 The formal methods are called inferential statistics.
 Statistical inference uses probability to determine how confident we can be that the conclusions are correct.
 If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life.

 The sampling distribution of a statistic is the distribution of the statistic for all possible samples from the same population of a given size.
 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.
 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 $n$.
 This statistic is then called the sample mean.

 Sampling distributions are important for inferential statistics.
 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:
 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.

 Any other number we choose to compute also counts as a descriptive statistic for the data from which the statistic is computed.
 Descriptive statistics are just descriptive.
 Generalizing from our data to another set of cases is the business of inferential statistics, which you'll be studying in another section.
 Here we focus on (mere) descriptive statistics.
 Some descriptive statistics are shown in Table 1.

 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.