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=800, and p^=0.217 with SE=0.01.

Required:
Find the value of the standardized z-test statistic.

Answer 1

Z = -6.3

Explanation:

Given that:

`\mathbf{H_o :p= 0.28}`

`\mathbf{H_o :p < 0.28}`

Since the alternative hypothesis is less than 0.28, then this is a left-tailed hypothesis.

Sample sixe n = 800

`\hat p` = 0.217

The standard error
`S.E(p) = \sqrt{(p(1-p))/(n)}`

`S.E(p) = \sqrt{(0.28(1-0.28))/(800)}`

`S.E(p) \simeq0.015`

Since this is a single proportional test, the test statistics can be computed as:

`Z = \frac{\hat p - p}{\sqrt{(p(1-p))/(n)}}`

`Z = (0.217- 0.28)/(0.01)`

Z = -6.3