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 \(\bar{X}=19.86\) 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 (Ho 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.