Multiple Choice
Which of the following correctly represents the sample space for a single toss of a fair coin?
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4. Probability
Basic Concepts of Probability
Multiple Choice
Which of the following statements about the population proportion and sample proportion is correct?
A
The population proportion is calculated only from the sample data.
B
The population proportion and sample proportion always have the same value.
C
The sample proportion is always greater than the population proportion .
D
The sample proportion is an estimate of the population proportion and may differ from it.
Verified step by step guidance1
Understand the definitions: The population proportion (usually denoted as \(p\)) is the true proportion of a characteristic in the entire population, which is generally unknown and fixed.
Recognize that the sample proportion (denoted as \(\hat{p}\)) is calculated from sample data and serves as an estimate of the population proportion.
Note that the sample proportion \(\hat{p}\) is computed as \(\hat{p} = \frac{x}{n}\), where \(x\) is the number of successes in the sample and \(n\) is the sample size.
Understand that because the sample is only a subset of the population, \(\hat{p}\) can vary from sample to sample and may be greater than, less than, or equal to the true population proportion \(p\).
Conclude that the correct statement is: the sample proportion is an estimate of the population proportion and may differ from it, reflecting sampling variability.
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