What sample size should we select if we wish to develop a 90% confidence interva

Question

What sample size should we select if we wish to develop a 90% confidence interval for the average diameter of the washers produced by our company, yet we wish to have a margin of error of no more than 0.035 mm? Assume our manufacturing process results in a standard deviation of 0.2.

5. An association wishes to design and conduct a poll to determine the proportion of Americans who oppose a law limiting the sale of handguns. If they wish to be 94% confident that their sample results differ from the true population proportion by no more than 0.07, what is the smallest size they should use?

Explanation / Answer

a.
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.1% LOS is = 1.64 ( From Standard Normal Table )
Standard Deviation ( S.D) = 0.2
ME =0.035
n = ( 1.64*0.2/0.035) ^2
= (0.328/0.035 ) ^2
= 87.824 ~ 88      
b.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.06 is = 1.881
Sample Proportion = 0.5
ME = 0.07
n = ( 1.881 / 0.07 )^2 * 0.5*0.5
= 180.518 ~ 181

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