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Actually I'm a bit confused how to choose my NULL hypothesis and how to choose the alternative one. suppose I have a sample of salary with mean 112,000 and I want to check if the population has mean greater than 112,000$ , what will be my NULL hypothesis?.

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  • $\begingroup$ The thing you want to show is the alternative hypothesis. It's contrary the null hypothesis. If you are unsure, maybe a two sided test would be more appropriate. $\endgroup$
    – Michael M
    Aug 9, 2019 at 16:41
  • $\begingroup$ So in my example the Null hypothesis is the mean less than 112,000 $ !? $\endgroup$ Aug 9, 2019 at 16:44

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Plenty of sttistics teachers, particularly in intro classes (say AP stat), will write $H_0: \mu = 0$ vs $H_a: \mu <0$, but it's really $H_0: \mu \ge 0$ vs $H_a: \mu <0$.

The choice of null and alternative hypothesis is exactly that: a choice. A lawmaker may want to know if tax reform caused a decrease in inequality. If the tax reform increased inequality, sure, that contradicts $H_0: \mu = 0$, but it's not the desired effect. It's actually worse than doing nothing at all. Similarly, if you only care about whether or not two parameters are the same, the two-sided test would be appropriate.

It's completely dependent on your research question.

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  • $\begingroup$ so my desired effect is the alternative hypothesis !? $\endgroup$ Aug 9, 2019 at 17:05
  • $\begingroup$ @AbdEl-RahmanAkram yes but here you will see very soon what the issue is.... write down the test appropriately and it’s statistic and look at what happens. Hint: if the sample mean is assumed to be the best representation of the population mean and the deviation from that mean in the population have a certain distribution, then build the statistic and see what its value is..I’ll help you: the test becomes H0 m=112000 vs H1 m>112000, then do the calculations :-) $\endgroup$
    – Fr1
    Aug 9, 2019 at 17:12
  • $\begingroup$ @Fr1 in my example in the question is the null hypothesis is the mean less than 112,000 $? $\endgroup$ Aug 9, 2019 at 17:15
  • $\begingroup$ @AbdEl-RahmanAkram no the alternative is more than 112000 $\endgroup$
    – Fr1
    Aug 9, 2019 at 17:16
  • $\begingroup$ @Fr1 is that differs from what i said !?. $\endgroup$ Aug 9, 2019 at 17:20

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