Statistical Hypothesis

AKA: Research Hypothesis.
Context:
- It can (often) be an input to a Statistical Hypothesis Testing Task.
- It can range from being a Simple Hypothesis to being a Composite Hypothesis.
- It can range from being a Null Hypothesis to being an Alternate Statistical Hypothesis.
- It can range from being an Accepted Statistical Hypothesis to being a Rejected Statistical Hypothesis.
- It can range from being a True Statistical Hypothesis to being a Negative Statistical Hypothesis.
Example(s):
- the population mean is less than 0.3.
- the population mean is equal to 0.3.
- the sample data are normally distributed
- the population means are equal
- the population variances are equal.
- …
Counter-Example(s):
- an Accuracy Estimate.
- Significance Level.
- Test Statistic.
- Estimation.
- P-Value.
See: Neyman–Pearson Lemma, Test Statistic, Statistical Hypothesis Test Sensitivity, Bayesian Inference, Frequentist Inference, Population Sample.

References

(Encycplopedia of Mathematics, 2016) ⇒ Statistical hypothesis. © 2011, Encyclopedia of Mathematics Retrieved October 11, 2016, from http://www.encyclopediaofmath.org/index.php?title=Statistical_hypothesis&oldid=13484
- QUOTE: A specific assumption on the properties of a probability distribution that underlies observable random phenomena. The results of observations are usually represented as the realization of a number of random variables, whether finite or infinite. The joint distribution of these random variables is thus not completely known, and it is assumed in a statistical hypothesis that it belongs to a certain specific class of distributions. The problem of statistical hypotheses testing (cf. Statistical hypotheses, verification of) arises in this type of situation.

(Leard Statistics, 2016) ⇒ "Hypothesis Testing - Structure and the Research, Null and Alternative Hypothesis" Laerd Statistics, © 2013 Lund Research Ltd, n.d. Web. Retrieved October 11, 2016, from http://statistics.laerd.com/statistical-guides/hypothesis-testing.php
- QUOTE: (...) The first step in hypothesis testing is to set a research hypothesis. In Sarah and Mike's study, the aim is to examine the effect that two different teaching methods – providing both lectures and seminar classes (Sarah), and providing lectures by themselves (Mike) – had on the performance of Sarah's 50 students and Mike's 50 students. More specifically, they want to determine whether performance is different between the two different teaching methods. Whilst Mike is skeptical about the effectiveness of seminars, Sarah clearly believes that giving seminars in addition to lectures helps her students do better than those in Mike's class. This leads to the following research hypothesis:

Research Hypothesis: When students attend seminar classes, in addition to lectures, their performance increases.

(...) The best way to determine whether a statistical hypothesis is true would be to examine the entire population. Since that is often impractical, researchers typically examine a random sample from the population. If sample data are not consistent with the statistical hypothesis, the hypothesis is rejected.

There are two types of statistical hypotheses.

Null hypothesis. The null hypothesis, denoted by H0, is usually the hypothesis that sample observations result purely from chance.
Alternative hypothesis. The alternative hypothesis, denoted by H1 or Ha, is the hypothesis that sample observations are influenced by some non-random cause.