Q R1.4. Is there a relationship between ... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

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} 脳 100 = \frac{78 + 49 + 21}{78 + 4 + 49 + 21 + 21 + 46} 脳 100 = \frac{148}{219} 脳 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. $(P e r c e n t a g e o f Y o u n g e r F a c e b o o k) = \frac{Y o u n g e r r e s p o n d e n t s w i t h Y e s}{T o t a l y o u n g e r s t u d e n t s} 脳 100 = \frac{78}{78 + 4} 脳 100 = \frac{78}{82} 脳 100 鈮� 95.12$

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