Select the correct answer.
Which statement is true?
A. A sample statistic can never be equal to the population parameter.
B. Point estimates are defined for both samples and populations.
D. To calculate a sample proportion, we need to know the population size.
Answer (2)
Statement A is false: Sample statistics can equal population parameters.
Statement B is false: Point estimates are for samples, not populations.
Statement C is false: Sample proportion doesn't require population size.
Statement D is true: Calculating a point estimate requires the sample size. Therefore, the answer is D .
Explanation
Analyze the statements Let's analyze each statement to determine which one is true.
Evaluate Statement A Statement A: A sample statistic can never be equal to the population parameter. This is false because a sample statistic is an estimate, and it's possible for the estimate to match the actual population parameter, especially if the sample is representative.
Evaluate Statement B Statement B: Point estimates are defined for both samples and populations. This is false. Point estimates are calculated from sample data to estimate population parameters. They are not defined for populations themselves because the population parameter is the true value.
Evaluate Statement C Statement C: To calculate a sample proportion, we need to know the population size. This is false. A sample proportion is calculated by dividing the number of successes in the sample by the sample size. The population size is not needed.
Evaluate Statement D Statement D: To calculate a point estimate, we need to know the sample size. This is true. A point estimate is a single value estimate of a population parameter, and its calculation depends on the sample data, including the sample size. For example, the sample mean, a point estimate of the population mean, requires the sample size in its calculation.
Conclusion Therefore, the correct answer is statement D.
Examples
In quality control, a manufacturer might take a sample of products to estimate the proportion of defective items. The sample size is crucial for calculating this point estimate. Similarly, political polls use sample sizes to estimate the proportion of voters who support a particular candidate. Understanding these concepts helps in making informed decisions based on data.
After evaluating all provided statements regarding sample statistics and point estimates, Statement D is true, as calculating a point estimate requires knowledge of the sample size. The other statements were found to be false. Therefore, the correct choice is Statement D.
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