1. In hypothesis testing, the only two legitimate outcomes are either to not reject the null hypothesis or to reject the null hypothesis and accept the alternate hypothesis. Notice that the first conclusion specifically does not say to accept the null hypothesis. Why not?
2. In all of the cases we discussed the hypothesized difference in the mean was zero. Would it be possible to have a hypothesized difference of something other than zero? If so can you think of an example?
1. The first conclusion specifically does not say to accept the null hypothesis because the test is based on the claim which is the alternative hypothesis and if we are rejecting the null hypothesis that means we are accepting the alternative hypothesis but if we do not reject the null hypothesis that means we are not accepting the null hypothesis it does not refer to null hypothesis. The null hypothesis is assumed against the alternative and considered true hence we are only interested in rejecting or not rejecting it instead of accepting as acceptance is assumed.
2. Yes, it is possible to have a hypothesized difference of something other than zero. For example, we can hypothesize that the difference between the average weight of lions and the average weight of lionesses is 2 kgs.
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