- Describe the logic by which it can be concluded that someone can distinguish
between two things
- State whether random assignment ensures that all uncontrolled sources
of variation will be equal
- Define precisely what the probability is that is computed to reach
the conclusion that a difference is not due to chance
- Distinguish between the probability of an event and the probability
of a state of the world
- Define "null hypothesis"
- Be able to determine the null hypothesis from a description of an experiment
- Define "alternative hypothesis"
The Null Hypothesis

The hypothesis that an apparent effect is due
to chance is called the null hypothesis.
In the Physicians' Reactions example, the null hypothesis is that
in the population of physicians, the mean time expected to be
spent with obese patients is equal to the mean time expected to
be spent with average-weight patients. This null hypothesis can
be written as:

μobese = μaverage

or as

μobese - μaverage
= 0.

The null hypothesis in a correlational study
of the relationship between high-school grades and college grades
would typically be that the population correlation is 0. This
can be written as

ρ = 0

where ρ is the population correlation (not
to be confused with r, the correlation in the sample).

The probability value is the probability
of an outcome and not the probability of a particular
state of the world. In statistics, it is conventional to refer
to possible states of the world as hypotheses since
they are hypothesized states of the world. Using this terminology,
the probability value is the probability of an outcome given
the hypothesis. It is not the probability of the hypothesis given
the outcome.

Although the null hypothesis is usually that the
value of a parameter is 0, there are occasions on which the
null hypothesis is a value other than 0. For example, if one
were testing whether a subject differed from chance in their
ability to determine whether a flipped coin would come up heads
or tails, the null hypothesis would be that π =
0.5.

Keep in mind that the null hypothesis is typically
the opposite of the researcher's hypothesis. In the Physicians'
Reactions study, the researchers hypothesized that physicians
would expect to spend less time with obese patients. The null
hypothesis that the two types of patients are treated identically
is put forward with the hope that it can be discredited and therefore
rejected. If the null hypothesis were true, a difference as large
or larger than the sample difference of 6.7 minutes would be very
unlikely to occur. Therefore, the researchers rejected the null
hypothesis of no difference and concluded that in the population,
physicians intend to spend less time with obese patients.

If the null hypothesis is rejected, then the alternative
to the null hypothesis (called the alternative
hypothesis) is accepted. The alternative hypothesis is
simply the reverse of the null hypothesis. If the null hypothesis

μobese
= μaverage

is rejected, then there are two alternatives:

μobese
< μaverage

μobese
> μaverage.

Naturally, the direction of the sample means
determines which alternative is adopted. Some textbooks have
incorrectly argued that rejecting the null hypothesis that two
populations means are equal does not justify a conclusion about
which population mean is larger.