Question

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.

New attempt is in progress. Some of the new entries may impact the last attempt grading.Your answer is partially correct.

(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:		Enter your answer in accordance to item (a) of the question statement	to	Enter your answer in accordance to item (a) of the question statement
Comment on another’s post or status:		Enter your answer in accordance to item (a) of the question statement	to	Enter your answer in accordance to item (a) of the question statement
Comment on another user’s photo:		Enter your answer in accordance to item (a) of the question statement	to	Enter your answer in accordance to item (a) of the question statement
‘‘Like” another user’s content:		Enter your answer in accordance to item (a) of the question statement	to	Enter your answer in accordance to item (a) of the question statement
Send another user a private message:		Enter your answer in accordance to item (a) of the question statement	to	Enter your answer in accordance to item (a) of the question statement

Answer 1

• Step 1: Find ?/2

Level of Confidence = 95%
? = 100% - (Level of Confidence) = 5%
?/2 = 2.5% = 0.025

• Step 2: Find z_?/2

Calculate z_?/2 by using standard normal distribution (normal population with mean (?) = 0 and standard deviation (?) = 1)
with ?/2 = 0.025 as right-tailed area and left-tailed area.

z_?/2 = 1.96 (Refer z distribution table)

• Step 3: Calculate Confidence Interval

People who update status (p? =0.15)

Lower Bound = p? - z_?/2*?p?(1 - p?)/n = 0.15 - (1.96)*?[0.15(1 - 0.15)/970] = 0.15 - 1.96*0.0115 = 0.1275
Upper Bound = p? + z_?/2*?p?(1 - p?)/n = 0.15 + (1.96)*(0.0115) = 0.1725
Confidence Interval = (0.1275, 0.1725)

Comment on another's post or status (p? =0.22)

Lower Bound = p? - z_?/2•?p?(1 - p?)/n = 0.22 - (1.96)(0.0133) = 0.1939
Upper Bound = p? + z_?/2•?p?(1 - p?)/n = 0.22 + (1.96)(0.0133) = 0.2461
Confidence Interval = (0.1939, 0.2460)

Comment on another user's photo (p? =0.20)

Lower Bound = p? - z_?/2•?p?(1 - p?)/n = 0.2 - (1.96)(0.01284) = 0.1748
Upper Bound = p? + z_?/2•?p?(1 - p?)/n = 0.2 + (1.96)(0.012843225981358711) = 0.2252
Confidence Interval = (0.1748, 0.2252)

Like another user's conent (p? =0.26)

Lower Bound = p? - z_?/2•?p?(1 - p?)/n = 0.26 - (1.96)(0.01408) = 0.2324
Upper Bound = p? + z_?/2•?p?(1 - p?)/n = 0.26 + (1.96)(0.01408) = 0.2876
Confidence Interval = (0.2324, 0.2876)

Send another user a private message (p? =0.10)

Lower Bound = p? - z_?/2•?p?(1 - p?)/n = 0.1 - (1.96)(0.0096) = 0.0811
Upper Bound = p? + z_?/2•?p?(1 - p?)/n = 0.1 + (1.96)(0.0096) = 0.1189
Confidence Interval = (0.0811, 0.1189)