Example 1 Carolโs Cereal Company has been accused of under filling (on average) its 20 oz boxes of toasted oats. The evidence: A sample of 100 boxes produced an average weight of 19.9 oz with a standard deviation of 0.5 oz.
How strong is the evidence?
Assuming the true average really is 20 oz, what is the probability that a random sample of 100 boxes will average under 20 oz?
Assuming the true average really is 20 oz, what is the probability that a random sample of 100 boxes will average under 19.9 oz?
What should we conclude?