A sample of 100 students was taken from Victoria to analyse the results of a national Mathematics assessment. Is the sample size large enough to be a good representative of the entire population?
Question
A sample of 100 students was taken from Victoria to analyse the results of a national Mathematics assessment. Is the sample size large enough to be a good representative of the entire population?
Solution
The answer to this question depends on several factors.
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Population Size: The size of the total population of students in Victoria is not given. If the total population is very large, a sample size of 100 might not be representative.
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Sampling Method: The method used to select the 100 students can also affect representativeness. If the students were selected randomly and without bias, they are more likely to be representative of the entire population.
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Margin of Error: The acceptable margin of error also plays a role. If a high level of precision is required, a larger sample size might be needed.
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Confidence Level: The confidence level is the probability that the value of a parameter falls within a specified range of values. A higher confidence level requires a larger sample size.
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Variability: If the scores of the national Mathematics assessment are highly variable, a larger sample size may be needed to accurately represent this variability.
Without more information, it's difficult to definitively say whether a sample size of 100 is large enough to be a good representative of the entire population. However, in general, a sample size of 100 is often considered sufficient in statistics for some analyses.
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