Chapter 6, Section 1-CI, Exercise 025 What Do People Do on Facebook? In a survey

Question

Chapter 6, Section 1-CI, Exercise 025 What Do People Do on Facebook? In a survey of 2255 US adults, we learn that 970 of the respondents use the social networking site Facebook.1 Of the 970 Facebook users, the survey shows that on an average day: • 15 update their status • 22 comment on another’s post or status • 20 comment on another user’s photo • 26 ‘‘like” another user’s content • 10 send another user a private message. 1Hampton, K., Goulet, L., Rainie, L., and Purcell, K., ‘‘Social Networking Sites and Our Lives,” Pew Research Center, June 16, 2011. (a) For each of the bulleted activities, find a 90% confidence interval for the proportion of Facebook users engaging in that activity on an average day. Round your answers to three decimal places. Bulleted Activities Confidence Interval Update status: to Comment on another’s post or status: to Comment on another user’s photo: to ‘‘Like” another user’s content: to Send another user a private message: to SHOW HINT LINK TO TEXT (b) Is it plausible that the proportion commenting on another’s post or status is the same as the proportion updating their status? Yes No

Explanation / Answer

PART A.
• 90% CI For15 update their status
given that,
possibile chances (x)=15
sample size(n)=970
success rate ( p )= x/n = 0.0155
CI = confidence interval
confidence interval = [ 0.0155 ± 1.645 * Sqrt ( (0.0155*0.9845) /970) ) ]
= [0.0155 - 1.645 * Sqrt ( (0.0155*0.9845) /970) , 0.0155 + 1.645 * Sqrt ( (0.0155*0.9845) /970) ]
= [0.0089 , 0.022]

• 22 comment on another’s post or status
given that,
possibile chances (x)=22
sample size(n)=970
success rate ( p )= x/n = 0.0227
CI = confidence interval
confidence interval = [ 0.0227 ± 1.645 * Sqrt ( (0.0227*0.9773) /970) ) ]
= [0.0227 - 1.645 * Sqrt ( (0.0227*0.9773) /970) , 0.0227 + 1.645 * Sqrt ( (0.0227*0.9773) /970) ]
= [0.0148 , 0.0305]

• 20 comment on another user’s photo
given that,
possibile chances (x)=20
sample size(n)=970
success rate ( p )= x/n = 0.0206
CI = confidence interval
confidence interval = [ 0.0206 ± 1.645 * Sqrt ( (0.0206*0.9794) /970) ) ]
= [0.0206 - 1.645 * Sqrt ( (0.0206*0.9794) /970) , 0.0206 + 1.645 * Sqrt ( (0.0206*0.9794) /970) ]
= [0.0131 , 0.0281]

• 26 ‘‘like” another user’s content
given that,
possibile chances (x)=26
sample size(n)=970
success rate ( p )= x/n = 0.0268
CI = confidence interval
confidence interval = [ 0.0268 ± 1.645 * Sqrt ( (0.0268*0.9732) /970) ) ]
= [0.0268 - 1.645 * Sqrt ( (0.0268*0.9732) /970) , 0.0268 + 1.645 * Sqrt ( (0.0268*0.9732) /970) ]
= [0.0183 , 0.0353]

•10 send another user a private message.

given that,
possibile chances (x)=10
sample size(n)=970
success rate ( p )= x/n = 0.0103
CI = confidence interval
confidence interval = [ 0.0103 ± 1.645 * Sqrt ( (0.0103*0.9897) /970) ) ]
= [0.0103 - 1.645 * Sqrt ( (0.0103*0.9897) /970) , 0.0103 + 1.645 * Sqrt ( (0.0103*0.9897) /970) ]
= [0.005 , 0.0156]

PART B.
given that,
sample one, x1 =15, n1 =970, p1= x1/n1=0.0155
sample two, x2 =22, n2 =970, p2= x2/n2=0.0227
CI = (p1-p2) ± sqrt( p1 * (1-p1)/n1 + p2 * (1-p2)/n2 )
where,
p1, p2 = proportion of both sample observation
n1,n2 = size of both group
a = 1 - (confidence Level/100)
Za/2 = Z-table value
CI = confidence interval
CI = [ (0.0155-0.0227) ± 1.64 * 0.0062]
= [ -0.0174 , 0.003 ]

yes, proportion commenting on another’s post or status is the same as the proportion updating
their status

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