Estimation of True Proportion with 98 Percent Confidence

Question

A company manufacturing computer chips finds that 8% of all chips manufactured are defective.  Management is concerned that high employee turnover is partially responsible for the high defect rate.  In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year.  After training was implemented, a sample of 450 chips revealed only 27 defects.  Using a 1% significance level, is there evidence that the additional training effective in lowering the defect rate.

Refer to the data in the above question to answer the following.

• Construct a 95% confidence interval for where the true proportion of defective parts is located. Round your final answer to the nearest .1%.
• If the company wants to estimate the true proportion to within 3% with 98% confidence, what sample size should they take? Round your answer to the nearest whole part. Was their original sample of 450 sufficient to meet their desired margin of error?

Summary

This question belongs to statistics and discusses about lowering defect rate in a computer manufacturing company.

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