You are planning a survey for which the findings are to have the specified level

Question

You are planning a survey for which the findings are to have the specified level of confidence. How large should your sample be so that the margin of error is at most the specified amount? (Round your answers to the nearest whole number.)

96% level of confidence

(a) margin of error = 3%
  

(b) margin of error = 2%
  

(c) margin of error = 1%
  

(d) Comparing your answers to parts (a)-(c), what conclusion can be made regarding the margin of error and the sample size?

Larger margins of error require a larger sample size to a certain point, and after that point they may have a smaller sample size.

No conclusions can be made.    

Smaller margins of error require a larger sample size, and larger margins of error may have a smaller sample size.

Larger margins of error require a larger sample size, and smaller margins of error may have a smaller sample size.

Smaller margins of error require a larger sample size to a certain point, and after that point they may have a smaller sample size.

Explanation / Answer

a) margin of error E =0.03

for we do not know estimated proportion p=0.5

for 99% CI ; critical z =2.5758

therefore sample size n=p(1-p)*(z/E)2 =~1844

b)margin of error E =0.02

therefore sample size n=p(1-p)*(z/E)2 =~4147

c)margin of error E =0.01

sample size n=p(1-p)*(z/E)2 =~16588

d)

Smaller margins of error require a larger sample size, and larger margins of error may have a smaller sample size.

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