Question

A quality control engineer is interested in estimating the proportion of defective items coming off a production line. In a sample of 200 items, 28 are defective. a) Find the 95% confidence interval for the proportion of defectives from this production line b) Interpret the results (the interval) you got.

Answer 1

Solution:

a)

Sample size = n = 200

Numbe rof defectives = x = 28

Confidence level = 0.95

So α=0.05

Therefore, Zc = 1.96 ....Using excel formula, =ABS(NORMSINV(0.05/2))

The sample proportion is,

The 95% confidence interval for population proportion is,

Therefore, 95% confidence interval for population proportion is (0.092, 0.188)

b)

we are 95% confident that the true population proportion of defective items coming off a production line p is contained by the interval (0.092, 0.188).

Done