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Tossing coin produces random outcomes, which suggests that the answer is probabilistic. Beginning with the
presumption that the coin is fair, problem 1 can be solved. It later proceeds to logically deduce the numerical
probabilities for each possible count of “tails” after a toss resulting from 10 tosses. The possible counts are 0,1….,10.
The solution to problem 2 starts with an unfamiliar toss; we do not know if it is fair or biased. The search for an
answer is experimental: Flip the coin, observe the outcome, then assess the data to determine if they appear to
have been generated by a fair or biased toss. One possible approach to making this judgement would be the
following: Toss the coin 10 times and record the number of count when you got a “tail”. Throw the coin 100 more
times in this manner. Compile how many times each of these 100 trials resulted in a "tail". Compare these results to
the frequencies produced by the 30 mathematical models for a fair toss in problem 1. If the frequencies from the
experiment are quite dissimilar from those predicted by the mathematical model for a fair toss and the observed
frequencies are not likely to be due to chance variability, then we can conclude that the toss is not fair. In problem 1,
we form our answer from logical deductions. In problem 2, we form our answer by observing experimental results.
3.5. WHAT IS A SAMPLING ERROR?
A sampling error is a deviation in the sampled value versus the true population value. Because the sample is not
typical of the population or is skewed in some manner, sampling mistakes happen. Even randomised samples will
have some degree of sampling error because a sample is only an approximation of the population from which it
is drawn.
Sampling is an analysis performed by selecting a number of observations from a larger population. Both sampling
errors and non-sampling mistakes can be produced by the selection process. Even when there are no errors of any
type, a sampling error may occur; sampling errors occur because no sample will ever perfectly match the data in
the universe from which the sample is taken.
Company XYZ will also want to avoid non-sampling errors. Non-sampling errors are errors that result during data
collection and cause the data to differ from the true values. Human error, such as an error committed during the
surveying procedure, is what leads to non-sampling mistakes.
If one group of consumers only watches five hours of video programming a week and is included in the survey, that
decision is a non-sampling error. Asking questions that are biased is another type of error.
The formula of Sampling Error is as follows:
s
Sampling Error = Z ×
n
Where
Z = Z score value based on the confidence interval (approx = 1.96)
σ = Population standard deviation
n = Size of the sample
The overall sampling error in statistical analysis is calculated using the sampling error formula. The sampling error
is calculated by dividing the standard deviation of the population by the square root of the size of the sample, and
then multiplying the resultant with the Z score value, which is based on the confidence interval.
3.5.1. Understanding Sampling Errors
A statistical error known as a sampling error when they choose a sample that does not accurately reflect the
complete population of data. As a result, the sample's findings do not accurately reflect the findings from the total
population.
In general, sampling errors can be placed into four categories:
1. Population-Specific Error: A population-specific error occurs when the researcher does not understand
who they should survey. For example, a researcher commits a population-specific mistake if they don't know
who to survey.
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