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 .

a) 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.

b) Based on your answer to part b, should you choose α = 0.01 or α = 0.10?

Answer 1

Claim is that the peanut butter manufacturer is shorting customers by under filling the jars, i.e. the mean content is less than 32 ounces

(A) This claim will be the alternate hypothesis that we need to test.

So, Null hypothesis is "the mean content is not less than 32 ounces"

Alternate hypothesis is "the mean content is less than 32 ounces"

(B) We know that type I error is rejecting the true null hypothesis and type II error is accepting the false null hypothesis.

Type I error in this case will be that "company is cheating customers even when it is not cheating" and type II error will be that "company is working fine even when company is cheating"

If we look at the error, type I error is more serious because it is not good to claim that the company is cheating, when everything is working fine in the company and its not cheating.

(C) I will choose lower value of alpha because alpha is the chances of making type I error. Thus, an alpha level of 0.01 has only 1% chance of making type I while an alpha level of 0.10 has 10% chances of making type I error.

So, alpha level of 0.01 is more favorable.