Lesson 3.4 – Estimating a Margin of Error
- Use simulation to approximate the margin of error for a sample proportion and interpret the margin of error.
- Use simulation to approximate the margin of error for a sample mean and interpret the margin of error.
Activity: How much TV do students watch?
Students are expected to do the first page of this Activity in pairs. The second page is done as a whole group. On the first page, we are trying to get students to see the reason why we multiply the standard deviation by 2 in order to get the margin of error. The reason is because a majority or our estimates will be within 2 standard deviations away from the mean (should be around 95%). Since our students have already seen the normal distribution and the 68-95-99 rule in their Algebra 2 class, we can also make this connection.
Mean – 2 * S.D. = 5.019 – 2 * 0.262 = 4.495
Mean + 2 * S.D. = 5.019 + 2 * 0.262 = 5.543
29 out of the 30 (97%) of the estimates are between 4.495 and 5.543 hours of TV.
On page two of the activity, we show students this calculation (which is really a 95% confidence interval…a preview of what’s to come!). We felt that we needed the idea of a confidence interval in order to discuss the margin or error. We worked as a whole group to take the students through the second example concerning the proportion of students who text during class.
As an exit slip, students worked individually on the application. The Application allows students a chance to try to write an interpretation of a margin of error on their own. It also gives them their first chance to assess whether a claim is plausible (is the claimed value within the confidence interval?). We like that students are already practicing inferential thinking before we have formally reached statistical inference.
We were very specific with how we wanted students to interpret the margin or error: “we expect the true proportion/mean (context) to be at most _______ away from our estimate of _________.”