Back to Estimate population parameters with margin of error — Problem 2 · Task Set 15

Exercises: Estimate a Population Mean or Proportion with a Margin of Error

Work through each section in order. Show your work where indicated. When you report an estimate, give the point estimate, the margin of error (about two standard deviations of the simulated sampling distribution), and the interval estimate, and interpret it in context.

Grade 11·21 problems·~45 min·Common Core Math - HS Statistics and Probability·group·hss-ic-b-4

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Recall / Warm-Up

A random sample of 60 students gives $\hat{p} = 0.65$ for the proportion who would re-enroll.
Which statement is the most honest report of what this tells us about the population proportion $p$ ?

Exactly 65% of all students would re-enroll.

$0.65$ is a point estimate of $p$ ; another random sample would likely give a somewhat different value, so the estimate needs a margin.

The sample is wrong because it did not survey every student.

$p$ must be between $0$ and $0.65$ .