Question

The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. Test H0: p 0.28 vs Ha: p 0.28 when the sample has n 900 , and p ^ 0.216 with SE 0.01 . Find the value of the standardized z -test statistic.

Answer 1

The value of the standardized z-test statistic is -6.4.

Explanation:

The test statistic is:

`z = (X - \mu)/(s)`

In which X is the sample mean,
`\mu` is the value tested at the null hypothesis, and s is the standard error.

0.28 is tested at the null hypothesis:

This means that
`\mu = 0.28`

p ^ 0.216 with SE 0.01

This means that
`X = 0.216, s = 0.01`

Then

`z = (X - \mu)/(s)`

`z = (0.216 - 0.28)/(0.01)`

`z = -6.4`

The value of the standardized z-test statistic is -6.4.