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Inferences based on Single Samples

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A consumer protection group is concerned that a ketchup manufacturer is filling its 20-ounce family-size containers with less than 20 ounces of ketchup. The group purchases 10 family-size bottles of this ketchup, weighs the contents of each, and finds that the mean weight is equal to 19.86 ounces, and the standard deviation is equal to 0.22 ounces.

-Do the data provide sufficient evidence for the consumer group to conclude that the mean fill per family-size bottle is less than 20 ounces? Test using alpha=0.05.

- If the test in part a were conducted on a periodic basis by the company's quality control department, is the consumer more concerned about making a Type I or Type II error? (consumer's risk)

-The ketchup company is also interested in the mean amount of ketchup per bottle. It does not wish to overfill them. For the test conducted in a, which type error is more serious from the company's point of view-Type I or Type II error? (producer's risk)

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