In: Statistics and Probability
A sample of 256 items is taken from an assembly line which
produces 10000 items per day. It is found
that 16 of the sampled items are defective. An approximate 95%
confidence interval for the proportion of
defectives produced that day is
Solution :
Given that,
Point estimate = sample proportion =
= x / n = 16 / 256 = 0.0625
Z/2
= 1.96
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
= 1.96 * (((0.0625
* 0.9375) / 256)
= 0.030
A 95% confidence interval for population proportion p is ,
- E < p <
+ E
0.0625 - 0.03 < p < 0.0625 + 0.03
00325 < p < 00925