Question

Please thoroughly explain each answer.

A manufacturer of computer chips has a computer hardware company as its largest customer. The computer hardware company requires all of its chips to meet specifications of 1.2 cm. The vice-president of manufacturing, concerned about a possible loss of sales, assigns his production manager the task of ensuring that chips are produced to meet the specification of 1.2 cm.

Based on the production run from last month, a 95% confidence interval was computed for the mean length of a computer chip resulting in:
95% confidence interval: (0.9 cm, 1.1 cm)

1. What are the elements that the production manager should consider in determining his company's ability to produce chips that meet specifications?
2. Do the chips produced meet the desired specifications?
3. What reasons should the production manager provide to the vice-president to justify that the production team is meeting specifications?
4. How will this decision impact the chip manufacturer's sales and net profit?

Answer 1

1).

The manager shoul consider the estimator, reliability coefficient, and standard error for determining the company's ability to produce ships that meet specifications, where, estimator is the point estimate of the population mean, reliability coefficient corresponds to z score for a suitable confidence interval, and standard error is the standard deviation of sampling distribution of sample means.

2).

In repeated sampling, for 95% of the intervals will contain the mean population value, that is 1.2. Therefore, it seems that chips produced do not meet the specifications.

3).

The vice president might site for an assumption of low cnfidence level, that is a low reliability coefficient. If a higher eliability coefficient is included, it might have led to a wider confidence interval to capture the population mean 1.2 cm.

4).

The chip manufacturer's sales and net profit might not be affected as inclusion of higher confidence level, keeping the same sample size will result into a much wider interval to capture the true population mean. Therefore, it will eventually state that with higher confidence level, the interval captures the true population mean, and thus meets specifications.

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