Chapter 1: Q R1.4. (page 76)

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?

Short Answer

Expert verified

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 $52.70 %$

Step by step solution

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.

P e r c e n t a g e o f F a c e b o o k U s e r s = \frac{R e s p o n s e s w i t h Y e s}{T o t a l r e s p o n s e s} \times 100 = \frac{78 + 49 + 21}{78 + 4 + 49 + 21 + 21 + 46} \times 100 = \frac{148}{219} \times 100 = 67.58 %

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. $(P e r c e n t a g e o f Y o u n g e r F a c e b o o k) = \frac{Y o u n g e r r e s p o n d e n t s w i t h Y e s}{T o t a l y o u n g e r s t u d e n t s} \times 100 = \frac{78}{78 + 4} \times 100 = \frac{78}{82} \times 100 \approx 95.12$

The following formula can be used to compute the percentage of younger Facebook users among all Facebook users. $(P e r c e n t a g e o f Y o u n g e r F a c e b o o k u s e r s a m o n g a l l F a c c b o o k u s e r s) = \frac{Y o u n g e r r e s p o n d e n t s w i t h Y e s}{T o t a l r e s p o n s e s w i t h Y e s} \times 100 = \frac{78}{78 + 49 + 21} \times 100 = \frac{78}{148} \times 100 = 52.70 %$