You want to create a 95% confidence interval with a margin of error of 3 more th

Question

You want to create a 95% confidence interval with a margin of error of 3 more than 0.05 for a population proportion. The historical data indicate that the population has remained constant at about 0.55. What is the minimum size random simple you need to construct this interval? 378 380 223 324 None of the above sample of size 8 is drawn from a population with an unknown distribution, and the sample mean Is calculated. If the mean of the population is 27 a standard deviation of 8.5, what is the probability the sample mean will be smaller an 20?

Explanation / Answer

1.

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.05  
p =    0.55  
      
Thus,      
      
n =    380.3044232  
      
Rounding,      
      
n =    381 [ANSWER, B is closest]

We usually round up in determining n, hence, 380.3-->381. However, if you simply round in your class, then please choose B. Thanks!

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