Question 2 Background: Facebook: Top Source for News A poll based on a random sa

Question

Question 2 Background: Facebook: Top Source for News A poll based on a random sample of 1,820 American adults (aged 18 and older, living in all 50 U.S. states and the District of Columbia) was conducted to study the source of news for Americans. The study reports that the proportion of all Americans who use Facebook as their source of news is estimated to be 61 %. Question 2 Subquestions 2.a Give a 99% conservative confidence interval for the proportion of all such Americans who would say Facebook is their source of news. Show all work. 2 point(s) No answer entered. Click above to enter an answer. 2.b The study went on to report the results by age group. If the results were used to make a 99% conservative confidence interval for the proportion of all Americans who are in their 30s (using only the subset of the 1820 Americans surveyed who are in their 30s), the corresponding margin of (sampling) error would have been... 1 point(s) points O smaller O larger

Explanation / Answer

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.61          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.011433035          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
Margin of error = z(alpha/2)*sp =    0.029449546          
lower bound = p^ - z(alpha/2) * sp =   0.580550454          
upper bound = p^ + z(alpha/2) * sp =    0.639449546          
              
Thus, the confidence interval is              
              
(   0.580550454   ,   0.639449546   ) [ANSWER]

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

b)

LARGER. [ANSWER]

Note that smaller sample sizes yield larger margin of error.

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

c)

RESPONSE BIAS. [ANSWER]

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

d)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.05  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
E =    0.03  
p =    0.61  
      
Thus,      
      
n =    715.1653197  
      
Rounding up,      
      
n =    716   [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.