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Statistics - One-tail , Two-tail , and Sampling Distribution

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A can of peeled tomatoes is supposed to contain an average of 19 ounces of tomatoes (excluding the juice). The actual weight is a normally distributed random variable whose standard deviation is known to be 0.25 ounces. (a) In quality control, would a one-tail or two-tailed test be used? Why? (b) Explain the consequences of departure from the mean in either direction. (c) Which sampling distribution would you use if samples of four cans are weighed? Why? (d) Set up a two-tailed decision rule for α = .01

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One tail, two-tail and sampling distribution is examined. A complete, neat and step-by-step solution is provided.

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(a) In quality control a two-tailed test for the mean weight of the tomatoes will be used because the company would like to

ensure that the mean weight (m) of the tomatoes is neither less than the stipulated 19 ounces nor ...

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