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I know you need to use hypothesis testing for this question but im not sure how to start?

A manufacturer needs a part to meet detailed specifications. He will not return shipments of the part as long as the mean volume is 2,200 cubic centimeters. To save time and expense, the manufacturer will randomly select 100 items of the shipment and use the sample mean to estimate the shipment mean. The manufacturer knows that sample data will sometimes lead to a rejection of a good batch but considers this mistake of returning an acceptable shipment tolerable if it occurs for no more than 5% of the shipments. Find a range of acceptable sample means that will accomplish this goal. (Based on past experience, according to the firm, the standard deviation of volume is about 150 cubic centimeters).

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1 Answer 1

You may construct a confidence interval based on the sample mean $\bar x$, for this problem, the $95\%$ confidence level would be $$\bar x \pm 1.96 \frac{\sigma}{\sqrt{n}} = \bar x \pm 1.96 \frac{150}{\sqrt{100}} $$ and then, if the confidence interval contains 2200, the manufacturer would not return the shipments.

Based on this, you will be able to calculate the maximum and minimum possible value for $\bar x$.

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