Canadian chefs who believe bite-size desserts are the most popular dessert item.

Question

Canadian chefs who believe bite-size desserts are the most popular dessert item. The Hyde Park Neighborhood Association Outreach Committee recently conducted a survey to learn more about the issues and concerns of the residents. In a random sample of 124 residents, 20 indicated that the main barrier to involvement in community events is scheduling conflicts.^30 Find a 90% confidence interval for the true proportion of residents who believe the main barrier to involvement in community events is scheduling conflicts. Suppose no prior estimate of P is known. How large a sample is necessary for the bound on the error of estimation to be 0.04 with confidence level 90%? When unemployment rises high school students face more competition from college

Explanation / Answer

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.161290323          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.033029283          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.054328335          
lower bound = p^ - z(alpha/2) * sp =   0.106961987          
upper bound = p^ + z(alpha/2) * sp =    0.215618658          
              
Thus, the confidence interval is              
              
(   0.106961987   ,   0.215618658   ) [ANSWER]

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

b)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.05  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
E =    0.04  
p =    0.5  
      
Thus,      
      
n =    422.7411647  
      
Rounding up,      
      
n =    423   [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

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