problem-8.5
problem-8.5
The normal approximation is said to be valid provided np and
n(1-p) are 5 or more. In this case p=.999 under H0 and
n=5,760, leaving n(1-p) just larger than 5. Assuming the
approximation produces accurate p-values, we have the one-sided
test, yielding
> prop.test(5731, 5760, p=.999, alt="less")
1-sample proportions test with continuity correction
data: 5731 out of 5760, null probability 0.999
X-squared = 89.87, df = 1, p-value < 2.2e-16
alternative hypothesis: true p is less than 0.999
...
This is a very small p-value, indicating that the data is
inconsistent with the null hypothesis.