Question

11.99 Of the quantities $p_1,p_2,x_1,x_2,{\hat{p}}_1,{\hat{p}}_2$, and ${\hat{p}}_{\mathrm{p}}$.
a. which represent parameters and which represent statistics?
b. which are fixed numbers and which are variables?

Short answer

(a) The parameters are $p_1$and $p_2$and statistics are $x_1,x_2,{\hat{p}}_1,{\hat{p}}_2,$and ${\hat{p}}_{\mathrm{p}}$.

(b) The fixed numbers are $p_1$and $p_2$, and variables are $x_1,x_2,{\hat{p}}_1,{\hat{p}}_2,$and ${\hat{p}}_p$.

Step-by-step solution

Part (a) Step 1: Given information

To find that which represent parameters and which represent statistics.

Part (a) Step 2: Explanation

Let, the quantities are $p_1,p_2,x_1,x_2,{\hat{p}}_1,{\hat{p}}_2$, and ${\hat{p}}_P$.
$p_1$and $p_2$are parameters in the sense that they are population proportions.
The statistics $x_1,x_2,{\hat{p}}_1,{\hat{p}}_2,$and ${\hat{p}}_P$are the other quantities.
Asa result, the parameters are $p_1$and $p_2$and statistics are $x_1,x_2,{\hat{p}}_1,{\hat{p}}_2,$and ${\hat{p}}_P$.

Part (b) Step 1: Given information

To find that which are fixed numbers and which are variables.

Part (b) Step 2: Explanation

Let, the quantities are $p_1,p_2,x_1,x_2,{\hat{p}}_1,{\hat{p}}_2$, and ${\hat{p}}_p$.
Since, $p_1$and $p_2$are fixed number.

The other variables $x_1,x_2,{\hat{p}}_1,{\hat{p}}_2$, and ${\hat{p}}_P$are variable as the sample proportions.

Then ${\hat{p}}_1,{\hat{p}}_2,$and ${\hat{p}}_P$dependent on the sample size and, $x_1$and $x_2$ variables.
As a result, the fixed numbers are $p_1$and $p_2$, and variables are $x_1,x_2,{\hat{p}}_1,{\hat{p}}_2,$and ${\hat{p}}_p$.