Tests of Proportions
In this applet, we simulate a series of hypothesis of tests for the value
of the parameter p in
a Bernoulli random variable. Each column of red and green marks represents
a sample of 30 observations.
``Successes'' are coded by green marks and ``failures'' by red marks. The
estimate for the parameter
p is then
p_hat = (1/30)*(X1+..X30)
We can test a hypothesis such as
H0: p = p0
against the alternative hypothesis
Ha: p > p0
by using the statistic
since n=30, this should be approximately normal under the null hypothesis.
The pink region in the applet represents the region in which the null hypothesis
would be rejected.
You should try:
The red dots represent the samples for which the null hypothesis would be
rejected, while the black
the effect of changing alpha
changing the form of the hypotheses
making p different from p0
dots represent those for which the null hypothesis would not be
rejected. Which decision is correct?