Question

11.98 Consider a hypothesis test for two population proportions with the null hypothesis $H_0:p_1=p_2$. What parameter is being estimated by the
a. sample proportion $p_1$?
b. sample proportion ${\hat{p}}_2$ ?
c. pooled sample proportion ${\hat{p}}_{\mathrm{p}}$ ?

Short answer

(a) The population proportions $p_1$are used to estimate the sample proportion ${\hat{p}}_1$.

(b) The population proportions $p_2$ are used to estimate the sample proportion ${\hat{p}}_2$.

(c) The sample proportion ${\hat{p}}_{\mathrm{p}}$is estimated by the population's proportions $p$.

Step-by-step solution

Part (a) Step 1: Given information

To find the parameter is being estimated by the sample proportion ${\hat{p}}_1$.

Part (a) Step 2: Explanation

The null hypothesis $H_0:p_1=p_2$ is used in the hypothesis test for two population proportions.
The hypothesis test is applied to two population proportions in this case.
The population proportions $p_1$can be used to determine the sample proportion ${\hat{p}}_1$.
As a result, the population proportions $p_1$are used to estimate the sample proportion ${\hat{p}}_1$.

Part (b) Step 1: Given information

To find the parameter is being estimated by the sample proportion ${\hat{p}}_2$.

Part (b) Step 2: Explanation

The null hypothesis $H_0:p_1=p_2$ is used in the hypothesis test for two population proportions.
The hypothesis test is applied to two population proportions in this case.
The population proportions $p_2$can be used to determine the sample proportion ${\hat{p}}_2$.
As a result, the population proportions $p_2$are used to estimate the sample proportion ${\hat{p}}_2$.

Part (c) Step 1: Given information

To find the parameter is being estimated by the pooled sample proportion ${\hat{p}}_{\mathrm{p}}$.

Part (c) Step 2: Explanation

The null hypothesis $H_0:p_1=p_2$ is used in the hypothesis test for two population proportions.
The hypothesis test is applied to two population proportions in this case.
$p$is the common value of the proportions $p_1$and $p_2$.
As a result, the population proportions $p$can be used to determine the sample proportion ${\hat{p}}_{\mathrm{p}}$.