A sample of 256 items is taken from an assembly line which produces 10000 items per...

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

Expert Solution

Solution :

Given that,

Point estimate = sample proportion = = x / n = 16 / 256 = 0.0625

Z_/2 = 1.96

Margin of error = E = Z_{/ 2} * $\sqrt$ (( * (1 - )) / n)

= 1.96 * ( $\sqrt$ ((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

orchestra answered 2 years ago

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