I\'m lost A researcher wishes to estimate, with 95% confidence, the population p

Question

I'm lost A researcher wishes to estimate, with 95% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. estimate must be accurate within 1% of the true proportion No preliminary estimate is available Find the minimum sample size needed Find the minimum sample size needed, Find the minimum sample size needed, using a prior study that found that 34% of the respondents said they think their president can control the price of gasoline Compare the results from parts (a) and (b). What is the minimum sample sue needed assuming that no poor information is available ? (Round up to the nearest whole number as needed ) What it the minimum sample size needed using a prior study that found that 34% of the respondents said they think their president can control the price of gasoline? (Round up to the nearest whole number as needed) How do the results from (a) and (b) compare? Having an estimate of the population proportion raises the minimum sample size needed. Having an estimate of the population proportion reduces the minimum sample size needed Having an estimate of the population proportion has no effect on the minimum sample size needed.

Explanation / Answer

a)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.01  
p =    0.5  
      
Thus,      
      
n =    9603.647052  
      
Rounding up,      
      
n =    9604   [answer]

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b)

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 =    0.01  
p =    0.34  
      
Thus,      
      
n =    8620.233594  
      
Rounding up,      
      
n =    8621   [answer]

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c)

OPTION B: Having an estimate of the population proportion REDUCES the minimum sample size required.

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