Chapter 1, Problem 4CRE

(a)

To determine

To find: the percentage of students who responded isFacebook users.

Answer to Problem 4CRE

There is no condition applied to calculate the percentage of the Facebook users, so this percentage is a part of marginal distribution.

Explanation of Solution

Given:

Facebook user
age	yes	no
Younger(18-22)	78	4
Middle (23-27)	49	21
Older(28 and up)	21	46

Calculation:

The percentage of the students who responded and Facebook users can be calculated as below

Percentage of Facebook Users $=\frac{\text{ Responses with Yes }}{\text{ Total responses }}\times 100$

  $\begin{array}{l}=\frac{78+49+21}{78+4+49+21+21+46}\times 100\hfill \\ =\frac{148}{219}\times 100\hfill \\ =67.58\%\hfill \end{array}$

As there, there is no condition applied to calculate the percentage of the Facebook users, so this percentage is a part of marginal distribution.

Conclusion:

Therefore, there is no condition applied to calculate the percentage of the Facebook users, so this percentage is a part of marginal distribution.

(b)

To determine

To identify: the percent of the younger students who areFacebook users.

Answer to Problem 4CRE

The percent of the younger students is $52.70\%$

Explanation of Solution

Calculation:

The percentage of the younger Facebook users among all younger students can be caiculated as below

  $\begin{array}{l}\left(\begin{array}{c}\text{ Percentage of Younger Facebook }\\ \text{ users among all younger students }\end{array}\right)=\frac{\text{ Younger respondents with Yes }}{\text{ Total younger students }}\times 100\\ =\frac{78}{78+4}\times 100\\ =\frac{78}{82}\times 100\\ \approx 95.12\end{array}$

Now, the percentage of the younger Facebook users among all Facebook users can be calculated as below.

  $\begin{array}{l}\left(\begin{array}{c}\text{ Percentage of Younger Facebook }\\ \text{ users among all Faccbook users }\end{array}\right)=\frac{\text{ Younger respondents with Yes }}{\text{ Total responses with Yes }}\times 100\\ =\frac{78}{78+49+21}\times 100\\ =\frac{78}{148}\times 100\\ =52.70\%\end{array}$

Conclusion:

Therefore, the percent of the younger students is $52.70\%$