**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.

**Application 3.4**

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.

**Notes**

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 _________.”