## Hypothesis Test

The process of determining ``yes'' or ``no'' from the outcome of experiment is called a*hypothesis test*. A widely used formalization of this procedure is due to Neyman and Pearson. Suppose that a researcher is interested in whether a new drug works. Then

*null hypothesis*may be that the drug has no effect --it is often the reverse of what he or she actually believe, why? Because the researcher hopes to reject the hypothesis and announce that the new drug leads to

*significant*improvements. If the null hypothesis is not rejected, the researcher announces nothing and goes on to a new experiment.

Here we are interested in the plausibility of the hypothesis

regarding the ``true'' population mean .
is called an *alternative hypothesis*,
and together with the *null value* it forms the basis of hypothesis testing.
The null hypothesis
is used in the context of determining
whether we can reject `` in favor of .''

The test procedure, known as t-test,
is based upon the sample mean
and the sample standard deviation
from a data set of size .
Then the discrepancy between the sample mean and the ``assumed''
null value of population mean is measured by the *test statistic*

The significance level has to be chosen from 0.01 or 0.05 ( 0.1 is not common in this particular test). Under the null hypothesis , it is ``unlikely'' that the t-statistic lies in the critical region specified in the table below. If so, it suggests significant evidence against the null hypothesis in favor of .

Alternative hypothesis | Critical region to reject |

Alternatively, the p-value can be calculated so that ``p-value '' is equivalent to the t-statistic being observed in the critical region. When the null hypothesis is rejected (i.e., p-value ), it is reasonable to calculate the confidence interval estimating the population mean .