Question

select the correct answer.
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. fewer than 590 of all students must prefer coffee to tea.
b. more than 590 of all students must prefer coffee to tea.
c. the sample proportion must precisely represent the entire populations choice.
d. the population proportion is not necessarily equal to the sample proportion.

Explanation:

• Option A: The sample proportion is 59%, but the population proportion could be different. We can't say fewer than 590 (59% of 1000) must prefer coffee.
• Option B: Similarly, we can't conclude more than 590 must prefer coffee as the sample is just a subset.
• Option C: A sample proportion doesn't precisely represent the entire population; there's sampling variability.
• Option D: Since the sample is random, the population proportion (proportion of all 1000 students who prefer coffee) isn't necessarily equal to the sample proportion (59% from the random sample).

Answer:

D. The population proportion is not necessarily equal to the sample proportion.