How to be "random" in sample selection?

Well, no fixed criteria in statistics. Yes, there exist many theories and methodologies to create random sequences or numbers. However, this will depend on the population nature, situations and surrounding environment.

In general, we may think like following:

Many persons/machines to share in sample selection is better than to be done by only one. Diversity leads to better randomness.
Selecting in different times/situations/places is better than to do at once in order to get more randomness.
Changing methodologies/media of selection may help.
Combining two or more random samples create better random sample.

Anyway, since our goal is to get accurate inferences, we should try as possible to be randomized in sample selection.

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The "Sample"

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.

Conclusions of Hypothesis Testing

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Confidence Level and Confidence Interval

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

Test of Hypothesis

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