A sample of 225 whatzits is chosen at random from the day’s production and it is

Question

A sample of 225 whatzits is chosen at random from the day’s production and it is found that 198 meet specifications.

(a) Estimate the proportion of the day’s production that meets specifications and estimate the uncertainty of the first estimate (of the proportion).

(b) What is the smallest sample size which will guarantee, regardless of the characteristics of the new sample of that larger size that the uncertainty of the estimate (of the proportion of the day’s production that meets specifications) will be less than .003?

Explanation / Answer

a.
No. of success(x)=198
Sample Size(n)=225
Sample proportion = x/n =0.88
b.
For 99% CI
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.01 is = 2.576
Sample Proportion = 0.88
ME = 0.03
n = ( 2.576 / 0.03 )^2 * 0.88*0.12
= 778.598 ~ 779

For 95% CI
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Sample Proportion = 0.88
ME = 0.03
n = ( 1.96 / 0.03 )^2 * 0.88*0.12
= 450.748 ~ 451

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