Define the population and sample in your own words.
The population consists of a group similar objects or occurrences, which is a subject to study or experimental design for conclusive decisions. A sample is a small section of the population that can easily be worked with in experiments under the general assumption that the whole population will depict similar outcomes.
Explain the relationship between the sample and the population.
The common principle tying population and sample is; whereas a population consists of a whole set of the object under consideration, a sample is a subset of the same population under study, and in most cases, they show similar characteristics conclusively.
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Why is a Sample Used More often than a Population?
In most cases, the sample is studied than the population because the sample is easier to work with. Small sections of collected data are less prone to statistical errors and even faster to accomplish the desired goal of the study. A sample is also more convenient because it is a reflection of a lot bigger population that would be easier to study in case of a real-world problem.
Why is it Important to Consider Probabilities in Statistical Analysis?
It is important to consider probabilities in statistical studies because they help researchers anticipate the outcome of a particular trend in a population. Predictive studies can help in comparing the intended outcome with statistical results, thereby decreasing the chances of errors. Probabilities can also help in setting trends in a particular real-world problem, once a pattern is established.
Real-World Experimental Probability Problem
An example of an experimental probability would be as follows: Consider a four-digit combination of opening a safe. The first three digits of the combination are 1, 2, and 3, respectively. The other digits are 4, 5, 6, 7, 8, 9, and 0. A move consists of including the first three keys and then trying the last key out of all the keys (0 to 9) to safely open the safe. What is the probability that the last key would be one of the first three or one of the last seven?
