select the correct answer.\na survey of randomly - selected students on a campus of 1,000 students asked who…

select the correct answer.\na 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?\na. 590 students must prefer coffee to tea.\nb. less than 590 students must prefer coffee to tea.\nc. more than 590 students must prefer coffee to tea.\nd. the sample proportion must precisely represent the entire populations choice.\ne. the population proportion is not necessarily equal to the sample proportion.

select the correct answer.\na 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?\na. 590 students must prefer coffee to tea.\nb. less than 590 students must prefer coffee to tea.\nc. more than 590 students must prefer coffee to tea.\nd. the sample proportion must precisely represent the entire populations choice.\ne. the population proportion is not necessarily equal to the sample proportion.

Answer

Explanation:

Step1: Understand sampling concept

A sample proportion is an estimate. It doesn't mean the exact number in the population.

Step2: Analyze each option

  • Option A: Just because sample proportion is 59% doesn't mean exactly 590 out of 1000 students prefer coffee. There is sampling error.
  • Option B: We can't say less than 590 must prefer coffee.
  • Option C: We can't say more than 590 must prefer coffee.
  • Option D: A sample proportion doesn't precisely represent the population. There is always some uncertainty.
  • Option E: This is correct. A sample proportion is an estimate and the population proportion may be different due to sampling variability.

Answer:

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