Chapter 7.3, Problem 2E

Find p̂ and q̂ for each situation.

a. n = 60 and X = 35

b. n = 95 and X = 43

c. 68%

d. 55%

d. 12%

To determine

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

Answer to Problem 2E

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

Explanation of Solution

Given info:

$n=60$ and $X=35$.

Calculation:

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

$\begin{array}{c}\widehat{p}=\frac{X}{n}\\ =\frac{35}{60}\\ =0.58\end{array}$

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

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

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

To determine

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

Answer to Problem 2E

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

Explanation of Solution

Given info:

$n=95$ and $X=43$.

Calculation:

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

$\begin{array}{c}\widehat{p}=\frac{X}{n}\\ =\frac{43}{95}\\ =0.45\end{array}$

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 2E

The value of $\widehat{p}$ and $\widehat{q}$ is 0.68 and 0.32, respectively.

Explanation of Solution

Given info:

68%

Calculation:

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

$\begin{array}{c}\widehat{p}=\frac{X}{n}\\ =68\%\\ =\frac{68}{100}\\ =0.68\end{array}$

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

$\begin{array}{c}\widehat{q}=1-\widehat{p}\\ =1-0.68\\ =0.32\end{array}$

Thus, the value of $\widehat{p}$ and $\widehat{q}$ is 0.68 and 0.32, respectively.

To determine

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

Answer to Problem 2E

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

Explanation of Solution

Given info:

55%

Calculation:

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

$\begin{array}{c}\widehat{p}=\frac{X}{n}\\ =55\%\\ =\frac{55}{100}\\ =0.55\end{array}$

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

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

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

To determine

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

Answer to Problem 2E

The value of $\widehat{p}$ and $\widehat{q}$ is 0.12 and 0.88, respectively.

Explanation of Solution

Given info:

12%

Calculation:

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

$\begin{array}{c}\widehat{p}=\frac{X}{n}\\ =12\%\\ =\frac{12}{100}\\ =0.12\end{array}$

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

$\begin{array}{c}\widehat{q}=1-\widehat{p}\\ =1-0.12\\ =0.88\end{array}$

Thus, the value of $\widehat{p}$ and $\widehat{q}$ is 0.12 and 0.88, respectively