1 Interested in social experiments you want to estimate the

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.)

Solution

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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