Explain Type I and Type II errors in testing of Hypothesis

Types of hypothesis:

A proposition may take the form of asserting a causal relationship (such as "A causes B"). A proposition often (but not necessarily) involves an assertion of causation. For example, if a particular independent variable changes, then a certain dependent variable also changes. This formulation, also known as an "If and Then" statement, applies whether or not a proposition asserts a direct cause-and-effect relationship.

A hypothesis about possible correlation does not stipulate the cause and effect per se, only stating that "A is related to B". Investigators may have more difficulty in verifying causal relationships than other correlations, because quite commonly intervening variables also become involved, possibly giving rise to the appearance of a possibly direct cause-and-effect relationship, but which (upon further investigation) turn out to have some other, more direct causal factor not mentioned in the proposition. Also, a mere observation of a change in one variable, when correlated with a change in another variable, can actually mistake the effect for the cause, and vice-versa (i.e., potentially get the hypothesized cause and effect backwards).
Empirical hypotheses that experimenters have repeatedly verified may become sufficiently dependable that, at some point in time, they become considered as "proven". Some people may succumb to the temptation to term such hypotheses "laws", but they would do so mistakenly, since by definition a hypothesis explains and a law describes (for example, a law can state: "Matter can neither be created or destroyed, only changed in form"). More accurately, one could refer to repeatedly verified hypotheses simply as "adequately verified", or as "dependable".
Statistics features a rather more general concept of a hypothesis: this involves making assertions about the probability distributions or likelihoods of events.
Statisticians use two kinds of hypothesis: first, the null hypothesis or H0; secondly, the alternative hypothesis or H1. To give the simplest non-trivial example, one might formulate two hypotheses about tossing a coin:
• H0: coin-tossing operates "fairly" (equally likely to fall "Heads" or "Tails")
• H1: coin-tossing operates in a biased manner to give a 90% probability of falling "Heads"
No finite sequence of results could utterly falsify either hypothesis. However, various statistical approaches (such as Bayesian statistics and classical statistics (i.e. t-tests)) can quantify the strong intuition that H1 appears much less likely than H0 if, in 1,000 tosses, 495 came out "Heads" — and much more likely if 895 came out "Heads". In more complex sciences, researchers generally evaluate experiments statistically rather than as simple verifications or falsifications.
A hypothesis (from Greek ὑπόθεσις) consists either of a suggested explanation for a phenomenon or of a reasoned proposal suggesting a possible correlation between multiple phenomena. The term derives from the Greek, hypotithenai meaning "to put under" or "to suppose." The scientific method requires that one can test a scientific hypothesis. Scientists generally base such hypotheses on previous observations or on extensions of scientific theories.

Type I and Type II errors:
Rejecting a null hypothesis when it is true is called a Type I error, and its probability ( Which, as we have seen, is also the significance level of the test) is symbolized α (alpha). Alternatively, accepting a null hypothesis when it is false is called a Type II error, and its probability is symbolized β (beta). There is a trade-off between these two errors: the probability of making one type of error can be reduced only if we are willing to increase the probability of making the other type or error. With an acceptance region this small, we will rarely accept a null hypothesis when it is not true, but as a cost of being this sure, we will often reject a null hypothesis when it is true.
Put another way, in order to get a low β, we will have to put up with a high α. To deal with this trade-off in personal and professional situations, decision makers decide the appropriate level of significance by examining the costs or penalties attached to both types of errors.

When Type I error is preferred:
Suppose that making a Type I error (rejecting a null hypothesis when it is true) involves the time and trouble of reworking a batch of chemicals that should have been accepted. At the same time, making a Type II error (accepting a null hypothesis when it is false) means talking a chance that an entire group of users of this chemical compound will be poisoned. Obviously, the management of this company will prefer a Type I error to a Type II error and, as a result, will set very high levels of significance in its testing to get low β s.

When Type II error is preferred:
Suppose, on the other hand, that making a Type I error involves disassembling an entire engine at the factory, but making a Type II error involves relatively inexpensive warranty repairs by the dealers. Then the manufacturer is more likely to prefer a Type II error and will set lower significance levels in its testing.