9.7. Tests about a Population Proportion

The general setting is the following:

: the population proportion ;: the particular hypothesized value

The statistical description for a testing problem is

vs.

vs. ,

and

vs. .

General Procedure: Large Sample Case () and

level of significance

.

(I): vs. ,

Then,

In addition,

(II): vs. .

Then,

In addition,

(III): vs.

Then,

In addition,

Example 6:

An official of a large national union claims that the fraction of women in the union

is not significant different from 0.5,

vs. .

Using the sample information reported below,

Sample size	400
Women	168
Men	232

(a) Test the hypothesis at 5% level of significance using a critical value (classical approach).

(b) Test the hypothesis at 10% level of significance using a p-value.

(c) Using a confidence interval, test the hypothesis at the 5% level of significance.

[solutions:]

.

(a) ,

.

(b) ,

(c) A 95% confidence interval for is

Since , we reject .

JavaStatSoft:

Z test:

Statistics -> Tests -> One Sample -> Proportion and Count