Chapter 9.4, Problem 5E

(a)

To determine

To find: The $\overline{p}$ and $\overline{q}$.

Answer to Problem 5E

The values of $\overline{p}$ and $\overline{q}$ are 0.5 and 0.5, respectively.

Explanation of Solution

Given info:

$X_1=60$, $n_1=100$, $X_2=40$ and $n_2=100$.

Calculation:

The value of $\overline{p}$ is,

$\begin{array}{c}\overline{p}=\frac{x_1+x_2}{n_1+n_2}\\ =\frac{60+40}{100+100}\\ =\frac{\text{100}}{\text{200}}\\ =0.5\end{array}$

The value of $\overline{q}$ is,

$\begin{array}{c}\overline{q}=1-\overline{p}\\ =1-0.5\\ =0.5\end{array}$

Thus, the values of $\overline{p}$ and $\overline{q}$ are 0.5 and 0.5, respectively.

(b)

To determine

To find: The $\overline{p}$ and $\overline{q}$.

Answer to Problem 5E

The values of $\overline{p}$ and $\overline{q}$ are 0.5 and 0.5, respectively.

Explanation of Solution

Given info:

$X_1=22$, $n_1=50$, $X_2=18$ and $n_2=30$.

Calculation:

The value of $\overline{p}$ is,

$\begin{array}{c}\overline{p}=\frac{x_1+x_2}{n_1+n_2}\\ =\frac{22+18}{50+30}\\ =\frac{40}{\text{80}}\\ =0.5\end{array}$

The value of $\overline{q}$ is,

$\begin{array}{c}\overline{q}=1-\overline{p}\\ =1-0.5\\ =0.5\end{array}$

Thus, the values of $\overline{p}$ and $\overline{q}$ are 0.5 and 0.5, respectively.

(c)

To determine

To find: The $\overline{p}$ and $\overline{q}$.

Answer to Problem 5E

The values of $\overline{p}$ and $\overline{q}$ are 0.271 and 0.729, respectively.

Explanation of Solution

Given info:

$X_1=18$, $n_1=60$, $X_2=20$ and $n_2=80$.

Calculation:

The value of $\overline{p}$ is,

$\begin{array}{c}\overline{p}=\frac{x_1+x_2}{n_1+n_2}\\ =\frac{18+20}{60+80}\\ =\frac{38}{140}\\ =0.271\end{array}$

The value of $\overline{q}$ is,

$\begin{array}{c}\overline{q}=1-\overline{p}\\ =1-0.271\\ =0.729\end{array}$

Thus, the values of $\overline{p}$ and $\overline{q}$ are 0.271 and 0.729, respectively.

(d)

To determine

To find: The $\overline{p}$ and $\overline{q}$.

Answer to Problem 5E

The values of $\overline{p}$ and $\overline{q}$ are 0.243 and 0.757, respectively.

Explanation of Solution

Given info:

$X_1=5$, $n_1=32$, $X_2=12$ and $n_2=48$.

Calculation:

The value of $\overline{p}$ is,

$\begin{array}{c}\overline{p}=\frac{x_1+x_2}{n_1+n_2}\\ =\frac{5+12}{32+48}\\ =\frac{\text{17}}{\text{70}}\\ =0.243\end{array}$

The value of $\overline{q}$ is,

$\begin{array}{c}\overline{q}=1-\overline{p}\\ =1-0.243\\ =0.757\end{array}$

Thus, the values of $\overline{p}$ and $\overline{q}$ are 0.243 and 0.757, respectively.

(e)

To determine

To find: The $\overline{p}$ and $\overline{q}$.

Answer to Problem 5E

The values of $\overline{p}$ and $\overline{q}$ are 0.216 and 0.794, respectively.

Explanation of Solution

Given info:

$X_1=12$, $n_1=75$, $X_2=15$ and $n_2=50$.

Calculation:

The value of $\overline{p}$ is,

$\begin{array}{c}\overline{p}=\frac{x_1+x_2}{n_1+n_2}\\ =\frac{12+15}{75+50}\\ =\frac{27}{125}\\ =0.216\end{array}$

The value of $\overline{q}$ is,

$\begin{array}{c}\overline{q}=1-\overline{p}\\ =1-0.216\\ =0.794\end{array}$

Thus, the value of $\overline{p}$ and $\overline{q}$ is 0.216 and 0.794, respectively.