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 .22 ounce.

a. 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 a = .05

b. If the test in part a were conducted on a periodic basis by the company's quality control department.
is the consumer group more concerned about the company's making a Type I error or a Type I1 error?
(The probability of making this type of error is called the consumer's risk.)

c. 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 part

a, which type of error is more serious from the company's point of view-a Type I error or a Type I1 error? (The probability of making this type of error is called the producer's risk.)