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.
Given
Sample size, n=200
Number of defectives, x= 28
Proportion of defectives,
Since the requested confidence level is CL = 0.95, then α = 1 – CL = 1 – 0.95 = 0.05
= 0.025.
Then
So, the 95% confidence interval for the proportion of defectives from production line is given by:
a) (0.09198 , 0.18802)
b) Interpretation: Ninety-five percent of the confidence intervals constructed in this way would contain the true value for proportion of defectives from production line.
OR We are 95% confident that the proportion of defectives from production line is between 0.09198 and 0.18802.
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