Chapter 7.3, Problem 1E

In each case, find p̂ and q̂.

a. n = 80 and X = 40

b. n = 200 and X = 90

e. n = 130 and X = 60

d. 25%

e. 42%

To determine

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

Answer to Problem 1E

The value of $\widehat{p}$ and $\widehat{q}$ is 0.5 and 0.5, respectively.

Explanation of Solution

Given info:

$n=80$ and $X=40$.

Calculation:

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

$\begin{array}{c}\widehat{p}=\frac{X}{n}\\ =\frac{40}{80}\\ =0.5\end{array}$

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

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

Thus, the value of $\widehat{p}$ and $\widehat{q}$ is 0.5 and 0.5, respectively.

To determine

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

Answer to Problem 1E

The value of $\widehat{p}$ and $\widehat{q}$ is 0.45 and 0.55, respectively.

Explanation of Solution

Given info:

$n=200$ and $X=90$.

Calculation:

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

$\begin{array}{c}\widehat{p}=\frac{X}{n}\\ =\frac{90}{200}\\ =0.45\end{array}$

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

$\begin{array}{c}\widehat{q}=1-\widehat{p}\\ =1-0.45\\ =0.55\end{array}$

Thus, the value of $\widehat{p}$ and $\widehat{q}$ is 0.45 and 0.55, respectively.

To determine

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

Answer to Problem 1E

The value of $\widehat{p}$ and $\widehat{q}$ is 0.46 and 0.54, respectively.

Explanation of Solution

Given info:

$n=130$ and $X=60$.

Calculation:

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

$\begin{array}{c}\widehat{p}=\frac{X}{n}\\ =\frac{60}{130}\\ =0.46\end{array}$

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

$\begin{array}{c}\widehat{q}=1-\widehat{p}\\ =1-0.46\\ =0.54\end{array}$

Thus, the value of $\widehat{p}$ and $\widehat{q}$ is 0.46 and 0.54, respectively.

To determine

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

Answer to Problem 1E

The value of $\widehat{p}$ and $\widehat{q}$ is 0.25 and 0.75, respectively.

Explanation of Solution

Given info:

25%

Calculation:

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

$\begin{array}{c}\widehat{p}=\frac{X}{n}\\ =25\%\\ =\frac{25}{100}\\ =0.25\end{array}$

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

$\begin{array}{c}\widehat{q}=1-\widehat{p}\\ =1-0.25\\ =0.75\end{array}$

Thus, the value of $\widehat{p}$ and $\widehat{q}$ is 0.25 and 0.75, respectively.

To determine

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

Answer to Problem 1E

The value of $\widehat{p}$ and $\widehat{q}$ is 0.42 and 0.58, respectively.

Explanation of Solution

Given info:

42%

Calculation:

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

$\begin{array}{c}\widehat{p}=\frac{X}{n}\\ =42\%\\ =\frac{42}{100}\\ =0.42\end{array}$

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

$\begin{array}{c}\widehat{q}=1-\widehat{p}\\ =1-0.42\\ =0.58\end{array}$

Thus, the value of $\widehat{p}$ and $\widehat{q}$ is 0.42 and 0.58, respectively.