Null and Alternative Hypotheses

Fine... Constructing a statistical hypothesis is mainly to define what's called the null and the alternative hypotheses. Mostly in academic life, students are given the hypothesis to test. But in research or real experiment, constructing the hypotheses correctly is such vital step toward inference or statistical decision.

Let's focus on hypotheses for population mean, for simplicity goals...

Null hypothesis is mainly our initial information or primary belief about the population. Let's consider the production of 500 ml bottles. The 500 ml is the mean capacity of bottles capacity. Since this is the information we know from previous knowledge, it will be our null hypothesis.

We write:

H0: Mu = 500

Note: null hypothesis always has equality sign!

Test for a hypothesis is usually done when we are worried that some factors affected the population, or population has changed for any possible reasons.
OK, so the null hypothesis is the information we know primarily before the suspected change. So, here come the alternative hypothesis to be defined. The alternative hypothesis is usually the region where we suspect or worry that population has changed into.

For bottles capacity example: the change in 500 ml bottle capacity (for any reason) is a bad issue to encounter. For production: it's bad that our bottles be either less than or greater than 500 ml. Lower capacity means unmatched regulations and higher means extra content added.

This is called two sided hypothesis because either change up/down is undesired. Thus, we define our alternative hypothesis as:

H1: Mu != 500 (!= here means not equal)

The other type of hypothesis is to be one sided, when we interested only in (> or <) in alternative hypothesis. In such cases, we suspect/only worried that some factors changed our population toward one direction (up only, down only).
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Test of Hypothesis

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