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I'm looking for explanation for the following exam question I got wrong on a stats course on Coursera. Unfortunately, the correct answer is not provided and the forums are barely haunted, so I don't have much hope of gaining insight there.

The question is:

Which of the following statement(s) is/are correct?

  • I. If you conduct a significance test you assume that the alternative hypothesis is true unless the data provide strong evidence against it.

  • II. The null hypothesis and the alternative hypothesis are always mutually exclusive.

(Options I, II, both, neither)

My understanding is (was) that both these are true, but that was rejected! Can anyone provide the answer/explanation for me?

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    $\begingroup$ Please add the self-study tag to this question and read the associated info. It would help if you could expand a bit in the question about why you thought that both statements were true. $\endgroup$
    – EdM
    Commented Jul 15, 2018 at 22:38
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    $\begingroup$ I would be correct if it were talking about the null hypothesis rather than the alternative hypothesis $\endgroup$
    – Henry
    Commented Jul 15, 2018 at 23:41
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    $\begingroup$ Aargh! I read that as "assume the null hypothesis is true", probably 17 different times! The power of expectation! Thank you @Henry $\endgroup$
    – James
    Commented Jul 16, 2018 at 10:38

1 Answer 1

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The correct response is that only II is true: 

I.  If you conduct a significance test you assume that the alternative hypothesis 
    is true unless the data provide strong evidence against it.

False - in any significance test, you must assume that the null hypothesis is true. After all, when we test for significance, we are concerned with some $\alpha$ value that represents the probability of a Type I error (i.e. rejecting a null hypothesis assuming that it is true). In calculating this probability, we can contextualize the likelihood of our observed data being meaningfully different (as opposed to being a result of chance).

Example - Suppose we are testing the likelihood of our coin being unfair and that we decide to flip it several times and track the proportion of times it lands on heads and the proportion of times it lands on tails.

The null hypothesis may be that the proportion of heads and tails are equal (.5 each).

The alternative hypothesis may be that they are unequal.

Significance testing can allow us to understand the probability that we make the wrong conclusion of the coin being unfair (e.g. because .58 of the outcomes were heads and .42 were tails) given that it's actually a fair coin.

II. The null hypothesis and the alternative hypothesis are always mutually 
    exclusive.

True - The null hypothesis and alternative hypotheses must be mutually exclusive (i.e. only one of the two can be true) and exhaustive (i.e. collectively represent all possible outcomes).

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