8.32 In a Pew Research Center survey of 960 Facebook users, 452 cited “seeing ph

Question

8.32 In a Pew Research Center survey of 960 Facebook users, 452 cited “seeing photos or videos” as a major reason why they use Facebook, while 298 cited “keeping up with news and current events” as a major reason why they use Facebook. (Source: “6 new facts about Facebook,” bit.ly/1lAmkv5.) a. Construct a 95% confidence interval estimate for the population proportion of Facebook users who cite “seeing photos or videos” as a major reason for why they use Facebook. b. Construct a 95% confidence interval estimate for the population proportion of Facebook users who cite “keeping up with news and current events” as a major reason why they use Facebook. c. Compare the results of (a) and (b).

Explanation / Answer

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.470833333          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.016109951          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.031574924          
lower bound = p^ - z(alpha/2) * sp =   0.439258409          
upper bound = p^ + z(alpha/2) * sp =    0.502408257          
              
Thus, the confidence interval is              
              
(   0.439258409   ,   0.502408257   ) [ANSWER]

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b)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.310416667          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.014932423          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.029267011          
lower bound = p^ - z(alpha/2) * sp =   0.281149656          
upper bound = p^ + z(alpha/2) * sp =    0.339683677          
              
Thus, the confidence interval is              
              
(   0.281149656   ,   0.339683677   ) [ANSWER]

**************************

c)

As we can see, the whole interval in part a) is larger than the values in interval b). Hence, we see that the proportion of those citing that seeing photos or videos as a major reason why they use Facebook is greater than those citing that keeping up with news and current events as a major reason why they use Facebook. [CONCLUSION]

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