Welcome to test of hypothesis

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Hello All

This will be the blog to understand statistical hypotheses testing!

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Confidence Level and Confidence Interval

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Being confident make one's self more reassured. Briefly, explanations below are for two sided confidence levels/intervals in order to simplify the idea. Saying " two sided " gives initial impression that there is something like two limits, yeah they are: upper and lower limits where the confidence interval lies in between. Example: Let's look at the population of a specific mobile phone model. Suppose we are now interested in the ' weight ' property. We found that weight property follows a normal distribution with mean value of 120 grams and a standard deviation of 1.4 grams. Weight ~ Normal (Mu, Sigma) = Normal (120, 1.4) This understanding means that majority of mobiles tested will weigh very closely to 120 grams. Yes, there should be fluctuations above and below the mean value but surely that still relatively close to mean value. Suppose a question: do you expect weights like: 121, 119.5, 122.1, 118.9? Answer: Yes , I surely expect such ...
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The Fact and the Hypothesis

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A good fact to submit is that we can't easily know the exact truth values/parameters of a population. Mostly, population parameters also change slightly by time and/or affected by different surrounding factors. Example: a production line for the 500 ml bottles is assumed to produce a population of bottles such that mean value of bottles capacity is exactly 500 ml. Nice, but what happens in realty? In realty, several factors will mostly affect the production: human factors, machine factors, environment temperature...etc. Also, each new bottle will contribute in the population mean value. This means a continuous slight change, either up or down, of the mean capacity. Here comes the hypothesis! As you see, the ground truth value for population mean is difficult to be exactly determined. However, we have general assumptions/expectations. OK, constructing a hypothesis should always be driven by our initial knowledge and expectations about the population. ...
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The "Sample"

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Anytime you aim to perform a study on the entire population, you will surely find that this task will be: Much time and/or efforts consuming as populations are normally huge . Impossible if the population is infinite (such as products). Here comes the role of taking samples. Yes! we just take a sample from the whole population, perform the study on the chosen sample, apply the results back to our population. This is the core of  inferential statistics because what we do is to infer parameters/properties of the population using information from a small sample. Well, this does not mean we will obtain 100% exact accurate estimations or inferences. But to be as close as possible, sample elements should be taken randomly ! At least, being random in sample selection will mostly include the diversity of information/facts within our population.
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