Question

An estimate of the percentage of the defectives in a lot of pins supplied by a vendor is desired to be within 1% of the true proportion at 90% confidence level.

(a) (3 pts) If the actual percentage of the defectives is known to be 4%, what is the minimum sample size needed for the study?

(b) (3 pts) If the actual percentage of the defectives is unknown, what is the minimum sample size needed for the study?

(c) (3 pts) If the actual percentage of the defectives is unknown and we double the margin of error (from 1% to 2%), what is the minimum sample size needed for the study?

Answer 1

At = 1-0.90 =0.10, critical value, = ABS(NORM.S.INV(0.10/2)) = 1.6449

Margin of error, E = 0.01

a) Proportion of defectives, p = 0.04

q = 1-p = 1-0.04 = 0.96

Sample size, n =

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b) If the proportion is unknown then we assume it 0.5

p=0.50, q=0.50

E = 0.01

Sample size, n =

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c) If the proportion is unknown then we assume it 0.5

p=0.50, q=0.50

E = 0.02

Sample size, n =