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# Engineer's Confidence Interval

1. A quality engineer is responsible for maintaining control of the bottling process in a beer factory. The goals is to maintain the intended volume (6 oz) with as little variation as possible. Since product sampled is not suitable for sale and becomes waste, it is very important to sample a minimal number of bottles. However, it is also important that the conclusions resulting from the sampling be statistically valid. The engineer intends to conduct sampling based on the concept of the central limit theorem.

2. It is known that the bottling equipment can fill product with a standard deviation of .02 oz. An initial sample of 25 bottles is selected for evaluation and the mean volume measured was 6.01 oz. Determine a 95% confidence interval for the mean of the current process.If the policy of the business is to "never give the customer less product than advertised (6 oz)", are you confident with the process as it is currently operating? Explain.

#### Solution Preview

m = 6, x-bar = 6.01, s = 0.02, n = 25

(a) The z- score for 95% confidence level is 1.96

Standard Error, ...

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