Question: A consumer protection group is concerned that a catsup manufacturer is filling its 20-ounce family-size containers with less than 20 ounces of catsup. The group purchases 10 family-size bottles of this catsup, weighs the contents of each, and finds that the sample mean weight \[\overline{x}=19.86\] ounces and the standard deviation is equal to 0.22 ounce.

 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 \[\alpha =0.01\] . Decide whether the normal distribution or the t-distribution should be used.

 A Type II error would occur if the family-size bottles of ketchup actually contain less than 20 ounces of ketchup, but the assumption is that the bottles are filled correctly ( \[{{H}_{0}}\] is not rejected). Consumers would receive underfilled ketchup bottles! Explain (in words) what a Type I error would be in the context of the ketchup company and consumers.

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Deliverable: Word Document