The elves of the mount wish to conduct a survey of their pick-axes in order to construct a 95% confidence interval about the proportion of pick-axes in need of repair. What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 21 percent of the pick-axes are in need of repair?
Solution :
Given that,
= 0.21
1 - = 1 - 0.21 = 0.79
margin of error = E = 10% = 0.10
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.96
Sample size = n = (Z/2 / E)2 * * (1 - )
= (1.96 / 0.10)2 * 0.21* 0.79
= 63.73
Sample size =64 rounded
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