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I am in a Stats class with a brilliant Professor that I unfortunately do not get everything they say and or do. I have a question of theirs that I would like to see how others address the answer to it. The question is below. I am having trouble connecting how to decipher a Type I and a Type II and how it should be set up, especially when the word "erroneously" are thrown in. Please help to explain the best ways to understand and interpret the answers for A and B. (please note I already have the answers, it's how to understand and process them that I need more comprehension of)

Question

The manufacturer of an over-the-counter pain reliever claims that its product brings pain relief to headache sufferers in less than 3.5 minutes.

A. What null hypothesis is Mary testing if she commits a type I error when she erroneously concludes the manufacturer's claim is correct?

B. What null hypothesis is Mary testing if she commits a type II error when she erroneously concludes the manufacture's claim is correct?

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    $\begingroup$ Please add the [self-study] tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. $\endgroup$
    – gung - Reinstate Monica
    Commented Nov 13, 2016 at 23:06

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A Type I means to postulate a non existing effect. The manufacturer claims there is an effect of pain relief. So when the error of agreeing with the manufacturer is of type 1, the null hypothesis must be that there isn't an effect.

B The manufacturer still claims pain relief and she is still wrong in agreeing with him. This time, this makes her commit a type II error, missing an existing effect. Therefore, the "effect" must be defined as absence of pain relieve and the null hypothesis be pain relief. This second case is very counterintuitive.

PS. This less than 3.5 minutes bit is meant as a hint at unilateral testing.

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    $\begingroup$ Please be cautious when answering [self-study] questions. Our policy is not to provide people with the answers to their homework problems, but only to provide hints to help them do their HW themselves. Our policies are detailed here. $\endgroup$
    – gung - Reinstate Monica
    Commented Nov 14, 2016 at 0:39

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