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I'm learning statistics and having hard times understanding hypothesis.

Suppose we are testing the hypothesis that sugar is linked to obesity. Which will be for what type of hypothesis. for example-
H0: Yes, sugar is linked to obesity and H1: No, sugar is not linked to obesity or
H0: No, sugar is not linked to obesity and H1: Yes, sugar is linked to obesity.

Another example(from an exam): "Select the hypothesis formulation and the corresponding best values for α, in a Judiciary Scenario so as to avoid punishing an innocent in lieu of which it’s okay to pronounce a real case of guilty as not guilty:"
answer is: H0 : Defendant is Innocent, H1 : Defendant is not Innocent, α = 1%

I'm confused between which condition to select for what hypothesis and also how to select confidence intervals.

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  • $\begingroup$ A couple of comments. Identifying the null and alternate hypotheses have nothing to do with what you expect to happen or what you want to happen or what would be interesting. So the null hypothesis is that the incomes of men and women are equal. We may not expect the null hypothesis to be true. And maybe we want the null hypothesis to be true. But these considerations don't help you identify the null hypothesis. For probably every test you'll be studying, the null is always that there is no association, no correlation, no difference between groups, and so on. $\endgroup$ – Sal Mangiafico Mar 11 at 9:09
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In statistics Null Hypothesis i.e. H0 usually states that two variables ( in your case sugar and obesity ) are not related or there is no association between them. So for this case, the correct hypothesis should be - H0: No, sugar is not linked to obesity H1: Yes, sugar is linked to obesity.

Since now it's easy for you to state the Null hypothesis, all other statements about variables association become part of H1, H2, .... Hn hypothesis.

Now talking about confidence intervals - This concept emerges from the case where you compare a set of hypothesis to figure out which one is correct. The way you do it is using data given to you in various forms. You draw conclusions by doing various hypothesis-testing/statistical measures. These conclusions involve calculating certain variables/numbers based on various formulae ( just for example sake: t-test etc ). Now, these calculated numbers help in rejecting or accepting a certain hypothesis. But since we make certain assumptions about the inference that we are trying to do ( assumptions can be w.r.t the data, model etc) we can never be 100% accurate. Hence we try to find out how sure we are about these calculations ( aka a notion of being confident i.e confidence interval ). So it will totally depend on cases like in medical diagnosis even being 99% sure is not enough hence you need to be REALLY CONFIDENT in this domain. But certain other domains might not be so rigorous and you could maybe go with 95,90 or even 85% confidence intervals.


Note: This is my first answer and I do hope I did a good job!

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  • $\begingroup$ That was a nice explanation. You said "In statistics Null Hypothesis i.e. H0 usually states that two variables are not related or there is no association between them". So, how does that relate to my second example: "Select the hypothesis formulation and the corresponding best values for α, in a Judiciary Scenario so as to avoid punishing an innocent in lieu of which it’s okay to pronounce a real case of guilty as not guilty:" answer is: H0 : Defendant is Innocent, H1 : Defendant is not Innocent, α = 1%. How do i select which belongs to what in this case. I'm confused because. $\endgroup$ – Naveen Kumar Mar 11 at 6:51
  • $\begingroup$ In statistics, H0 is usually assumed to be true and then tests are performed to either reject or accept the H0. Since it's mentioned that by default we assume the person is innocent hence not guilty, this means that the Null Hypothesis H0: Defendant is Innocent ( No relation between Defendant and Guilty ). Also you mentioned alpha = 1% , the formula relating alpha and confidence interval is : alpha + confidence = 1. Hence you will need to find out the 99% confidence interval in your case. $\endgroup$ – Axelius Mar 11 at 7:00
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In inferential statistics, the null hypothesis is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups. (e.g. sugar is not linked to obesity)

Testing (rejecting or disproving) the null hypothesis and thus concluding that there are grounds for believing that there is a relationship between two phenomena (e.g. sugar is linked to obesity) is the criteria for rejecting a null hypothesis.

The null hypothesis is generally assumed to be true until evidence indicates otherwise.

In you case it would be

Ho : Sugar is not linked to Obesity

Hi : Sugar is linked to Obesity

When your Probability value(p value) <= level of significance (alpa, usually 0.05),

We reject the null hypothesis, concluding sugar is linked to Obesity

Else we fails to reject the null hypothesis, concluding sugar is not linked to obesity

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  • $\begingroup$ that was a nice explanation. you said "the null hypothesis is a general statement or default position that there is no relationship between two measured phenomena". So, in my second example, it should be "H0: Defendant is not Innocent". But, it's the other way. Why and How? $\endgroup$ – Naveen Kumar Mar 11 at 6:56
  • $\begingroup$ @NaveenKumar The underlying meaning is defendant is not related to crime. So, Ho: Defendant is innocent $\endgroup$ – Shinigami Mar 11 at 7:25

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