Questions: A survey of randomly-selected students on a campus of 1,000 students asked who preferred coffee to tea. The sample proportion is found to be 59%. Which statement is true? A. The sample proportion must precisely represent the entire population's choice. B. The population proportion is not necessarily equal to the sample proportion. C. More than 590 of all students must prefer coffee to tea. D. Fewer than 590 of all students must prefer coffee to tea.

Evaluate the given statements about the sample proportion and population proportion.

Understanding the sample proportion

The sample proportion is \(59\%\), which means that in the randomly selected sample of students, \(59\%\) preferred coffee to tea. This is an estimate of the population proportion but does not guarantee exact equality.

Analyzing statement A

Statement A claims that the sample proportion must precisely represent the entire population's choice. This is incorrect because a sample proportion is an estimate and is subject to sampling variability. It does not guarantee exact representation of the population proportion.

Analyzing statement B

Statement B claims that the population proportion is not necessarily equal to the sample proportion. This is correct because the sample proportion is an estimate, and the true population proportion could differ due to sampling error.

Analyzing statement C

Statement C claims that more than 590 of all students must prefer coffee to tea. This is incorrect because the sample proportion is an estimate, and the actual number of students who prefer coffee could be higher or lower than 590.

Analyzing statement D

Statement D claims that fewer than 590 of all students must prefer coffee to tea. This is incorrect because the sample proportion is an estimate, and the actual number of students who prefer coffee could be higher or lower than 590.

The correct statement is \(\boxed{B}\).

The correct statement is \(\boxed{B}\).