A hypothesis test will be performed to test the claim that a
population proportion is less than 0.70. A sample size of 400 and
significance level of 0.025 will be used. If p = 0.62, find the
probability of making a type II error, β.
- Fill in the blanks below to
describe the sampling distribution of ??� assuming H0 is
true.
- Mean =
- Standard deviation =
- Shape:
- Sketch the sampling distribution
of ??�assuming H0 is true.
- Specify the rejection region when
??� is used as the test statistic. Locate the rejection region on
your graph from part a.
- Describe the sampling
distribution of ??� if p = .62.
- Mean =
- Standard deviation =
- Shape:
- On your graph from part a, sketch
the sampling distribution of ??� if p =.62.
- Find the probability of failing
to reject H0 if p is actually equal to .62. That is,
find the probability of making a Type II error if p = .62.
- Shade the area corresponding to
this probability on your graph.