1) Interested in social experiments, you want to estimate the percentage of US a

Question

1) Interested in social experiments, you want to estimate the percentage of US adults willing to sing karaoke in front of strangers. You want to be within 3 percentage points of the true proportion measure, based upon a 95% confidence level. What size sample is required?--(NOTE that no estimate of "p-hat" is given.)

2)A farmer needs to determine the mean weight of all eggs produced by her chickens after she changed their diets. A random sample of 200 eggs yields a mean of 1.92ounces. Based upon a desired 95% confidence level, determine the associated confidence interval.   (Assume a population standard deviation of 0.45 oz.)

Explanation / Answer

1.

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 =    0.03  
p =    0.5  
      
Thus,      
      
n =    1067.071895  
      
Rounding up,      
      
n =    1068   [ANSWER]

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