Question

11.95 Explain the basic idea for performing a hypothesis test, based on independent samples, to compare two population proportions.

Short answer

The process is the same for a one-tailed test, with the exception that the null hypothesis is rejected only when ${\hat{p}}_1$is too much smaller than ${\hat{p}}_2$for a left-tailed test, and only when ${\hat{p}}_1$is too much larger than ${\hat{p}}_2$for a right-tailed test.

Step-by-step solution

Given information

To compare two population proportions by explain the basic idea for performing a hypothesis test, based on independent samples.

Explanation

Independent samples and a hypothesis test
The main concepts for conducting a hypothesis test using independent samples are as follows:
For a two-tailed test:
(1) Samples are taken independently and randomly from the two populations under consideration.
(2) The proportions of the two samples ${\hat{p}}_1$and ${\hat{p}}_2$ are then compared.
(3) The null hypothesis is rejected if the proportions of the samples differ by too much; otherwise, the null hypothesis is not rejected.
The process is the same for a one-tailed test, except that in a left-tailed test, the null hypothesis is rejected only if ${\hat{p}}_1$ is too much smaller than ${\hat{p}}_2$, and in a right-tailed test, the null hypothesis is rejected only if ${\hat{p}}_1$ is too much larger than ${\hat{p}}_2$.