Q R1.4. - The Practice of Statistics for AP

Question

Is there a relationship between Facebook use and age among college students? The following two-way table displays data for the $219$ students who responded to the survey.

(a) What percent of the students who responded were Facebook users? Is this percent part of a marginal distribution or a conditional distribution? Explain.

(b) What percent of the younger students in the sample were Facebook users? What percent of the Facebook users in the sample were younger students? 

Step-by-Step Solution

Answer

Part (a) The percentage of Facebook users is calculated without any conditions, so it is a part of the marginal distribution.

Part (b) The percent of the younger students is $52.70\%$

Part (a) Step 1: Given information

The table is 

	Facebook user
age	yes	no
younger(18-22)	78	4
middle(23-27)	49	21
older(28 and up)	21	46

Part (a) Step 2: Concept

A statistical graph or chart is a visual representation of statistical data in graphical form.

Part (a) Step 3: Calculation

The following formula can be used to compute the percentage of students who answered and Facebook users. 

$$\begin{gathered} Percentage of Facebook Users= \frac{Responses with Yes}{Total responses }\times 100 \\ = \frac{78+49+21 }{78+4+49+21+21+46 }\times 100 \\ = \frac{148}{219}\times 100 \\ = 67.58\% \end{gathered}$$

Because no constraint is employed when calculating the proportion of Facebook users, this number is a part of the marginal distribution. 

Part (b) Step 1: Calculation

The following formula can be used to compute the percentage of younger Facebook users among all younger students. $$\begin{gathered} ( Percentage of Younger Facebook) =\frac{Younger respondents with Yes}{Total younger students}\times 100 \\ =\frac{78}{78+4}\times 100 \\ =\frac{78}{82}\times 100 \\ \approx 95.12 \end{gathered}$$

The following formula can be used to compute the percentage of younger Facebook users among all Facebook users. $$\begin{gathered} \left(Percentage of Younger Facebook users among all Faccbook users\right)=\frac{Younger respondents with Yes}{Total responses with Yes}\times 100 \\ =\frac{78}{78+49+21}\times 100 \\ =\frac{78}{148}\times 100 \\ = 52.70\% \end{gathered}$$

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