# 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.