Question

Federal law requires that a jar of peanut butter that is labeled as containing 32 ounces must contain at least

32 ounces. An independent consumer advocate feels that a certain peanut butter manufacturer is shorting

customers by under filling the jars so that the mean content is less than 32 ounces as stated on the label.

The hypotheses tested are Ho: u= 32 oz; H1: u<32 oz.

a) In the context of this example, describe type I and type II errors. Give lots of details.

b) If you owned the peanut better plant which type of error would you consider more serious (from a

business point of view)? Explain, giving lots of details.

c) Based on your answer to part b, should you choose

α = 0.01

or

α = 0.10?

Answer 1

a) Type I error is rejecting H0 when H0 is true, which means the consumer will feel that the content is less than 32 oz when the actual content sold in the box is at least 32 oz.

Similarly, Type II error is accepting H0 when H0 is false, which means the consumer will feel that the content is atleast 32 oz when the actual content sold in the box is less than 32 oz.

b) As a business executive, I should be worried about Type I error, because that is the time when I do the right thing by putting at least 32 oz in the box, but the customer thinks that I have not. This is a serious problem and may disrepute my company. If I don't put 32 oz but the customer can't detect it then there is no fear of losing the reputation.

c) As I should be worried about Type I error, so I will want Type I error to be really less, and alpha connects to type I error, so we would want alpha=0.01