A sample of 200 light bulbs was tested and it was found that

A sample of 200 light bulbs was tested and it was found that 11 were defective. Calculate a 95% confidence interval around this sample proportion.

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Solution

A sample of 200 light bulbs was tested and it was found that 11 were defective. Calculate a 95% confidence interval around this sample proportion.

Confidence Interval Estimate for the Proportion

Data

Sample Size

200

Number of Successes

11

Confidence Level

95%

Intermediate Calculations

Sample Proportion

0.055

Z Value

1.9600

Standard Error of the Proportion=sqrt(0.055*0.945/200)

0.0161

Interval Half Width =1.96*0.0161=

0.0316

Confidence Interval

Interval Lower Limit = ( 0.055 - 0.0316) =

0.0234

Interval Upper Limit= ( 0.055 + 0.0316) =

0.0866