Type I error occurs when the null hypothesis is true but rejected, likened to a false positive or 'crying wolf.' Type II error happens when the null hypothesis is false but accepted as true, similar to a false negative or failing to raise an alarm. These errors relate to hypothesis testing, with Type I error denoted by alpha (\alpha) and Type II error by beta (\beta), influencing the test's conclusion regarding the hypothesis.

1. looking for examples of type I and type II errors in hypothesis testing
Solution
Type I error A type I error, also known as an error of the first kind, occurs when
the null hypothesis (H0) is true, but is rejected. It is asserting something that is absent, a false hit.
A type I error may be compared with a so called false positive (a result that indicates that a given
condition is present when it actually is not present) in tests where a single condition is tested for.
Type I errors are philosophically a focus of skepticism and Occam's razor. A Type I error occurs
when we believe a falsehood.[1] In terms of folk tales, an investigator may be "crying wolf"
without a wolf in sight (raising a false alarm) (H0: no wolf). The rate of the type I error is called
the size of the test and denoted by the Greek letter alpha (alpha). It usually equals the
significance level of a test. In the case of a simple null hypothesis alpha is the probability of a
type I error. If the null hypothesis is composite, alpha is the maximum (supremum) of the
possible probabilities of a type I error. Type II error A type II error, also known as an error of
the second kind, occurs when the null hypothesis is false, but it is erroneously accepted as true. It
is missing to see what is present, a miss. A type II error may be compared with a so-called false
negative (where an actual 'hit' was disregarded by the test and seen as a 'miss') in a test
checking for a single condition with a definitive result of true or false. A Type II error is
committed when we fail to believe a truth.[1] In terms of folk tales, an investigator may fail to
see the wolf ("failing to raise an alarm"; see Aesop's story of The Boy Who Cried Wolf).
Again, H0: no wolf. The rate of the type II error is denoted by the Greek letter beta (beta) and
related to the power of a test (which equals 1-beta). What we actually call type I or type II
error depends directly on the null hypothesis. Negation of the null hypothesis causes type I and
type II errors to switch roles. The goal of the test is to determine if the null hypothesis can be
rejected. A statistical test can either reject (prove false) or fail to reject (fail to prove false) a null
hypothesis, but never prove it true (i.e., failing to reject a null hypothesis does not prove it true).