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Answer :
To address the question about the margin of error and population mean with respect to the size of the population, we need to understand a few concepts related to statistics, specifically about sampling and estimation.
Population Mean: This is the mean (average) of a characteristic across the whole population. In this case, the population mean of the data is given as 2.3 hours. Importantly, the population mean is a fixed value. Whether the population size changes or not, the population mean value remains the same unless the data about individual elements changes.
Margin of Error: This is the range that the sample mean is likely to fall within from the true population mean. It depends on factors like the sample size, variability in the data, and the confidence level.
Let's analyze each statement:
A. The margin of error would decrease if the population size doubled.
This statement is not accurate. The margin of error is primarily influenced by the sample size, not the population size. If the sample size remains the same while the population size doubles, the margin of error does not decrease because the precision of the sample estimate is not improved by increasing population size alone.
B. The margin of error would increase if the population size doubled.
This statement is also not correct. As mentioned before, the margin of error is not directly affected by the population size but by the sample size. Simply doubling the population does not increase the margin of error.
C. The population mean would be less accurate if the population size doubled.
This statement is incorrect as well. The population mean itself does not change in accuracy based solely on an increase in population size. The accuracy of the population mean as an estimation in sampling contexts depends on the sample and how representative it is, not on the overall population size.
Conclusion: None of these statements are true. The margin of error is about how well a sample mean estimates a population mean and is affected by factors like sample size, variance, and confidence level, not by changes in the population size itself.
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