Example 1 A manufacturer of electronic calculators is interested in estimating t

Question

Example 1

A manufacturer of electronic calculators is interested in estimating the fraction of defective units produced. A random sample of 800 calculators contains 10 defectives. Compute a 95% confidence interval for the proportion of defective calculators.

Example 2

A survey found that out of 200 workers, 168 said they were interrupted three or more times an hour by phone messages, faxes, etc. Find the 90% confidence interval of the population proportion of workers who are interrupted three or more times an hour.

Example 3

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent (more than 90 days overdue). For this quarter, the auditing staff randomly selected 400 customer accounts and found that 80 of these accounts were delinquent. Find a 95% confidence interval for the proportion of all delinquent customer accounts at this manufacturing company?

Explanation / Answer

1)
n = 800 , p = 10/800 = 0.0125 , q = 1 - p = 1 - 0.0125 = 0.9875

z value at 95% CI = 1.96

CI = p +/- z * sqrt(p * (1 - p)/n)
= 0.0125 +/- 1.96 * sqrt(0.0125 * 0.9875 / 800)
= (0.005, 0.020)

2)
n = 200 , p = 0.84 , q = 1 -p = 0.16

z value at 95% CI = 1.645

CI = p +/- z * sqrt(p * (1 - p)/n)
= 0.84 +/- 1.645 * sqrt(0.84 * 0.16 / 200)
= (0.797, 0.883)

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