Middlesex Community College | Prepared by: Stephen McDonald
Hypothesis Testing: Basic Concepts
In the field of statistics, a hypothesis is a claim about some aspect of a population. A hypothesis
test allows us to test the claim about the population and find out how likely it is to be true.
The hypothesis test consists of several components; two statements, the null hypothesis and the
alternative hypothesis, the test statistic and the critical value, which in turn give us the P-value
and the rejection region (๐ผ), respectively.
The null hypothesis, denoted as ๐ป0 is the statement that the value of the parameter is, in fact,
equal to the claimed value. We assume that the null hypothesis is true until we prove that it is
not.
The alternative hypothesis, denoted as ๐ป1 is the statement that the value of the parameter differs
in some way from the null hypothesis. The alternative hypothesis can use the symbols <, >,
๐๐ โ .
The test statistic is the tool we use to decide whether or not to reject the null hypothesis. It is
obtained by taking the observed value (the sample statistic) and converting it into a standard
score under the assumption that the null hypothesis is true.
The P-value for any given hypothesis test is the probability of getting a sample statistic at least as
extreme as the observed value. That is to say, it is the area to the left or right of the test statistic.
The critical value is the standard score that separates the rejection region (๐ผ) from the rest of a
given curve.
Types of Errors:
๏ท A Type I Error is incorrectly rejecting a true null hypothesis (false negative).
๏ท A Type II Error is incorrectly failing to reject an untrue null hypothesis (false positive).
๐ฏ๐ is actually true
๐ฏ๐ is actually false
Decision
Reject ๐ป0
Type I Error
๐(๐๐ฆ๐๐ ๐ผ ๐ธ๐๐๐๐)= ๐ผ
Correct Decision
Fail to Reject ๐ป0
Correct Decision
Type II Error
๐(๐๐ฆ๐๐ ๐ผ๐ผ ๐ธ๐๐๐๐)= ๐ฝ