Margin of Error

Margin of Error

Objectives:

Learning Objective: Students will calculate and interpret margin of error.

Language Objective: Students will express their reasoning in written form.

A study that analyzed scalp hair samples from 22 participants with epilepsy and 23 participants without epilepsy, checking for differences in levels of copper, iron, zinc, magnesium, and calcium. The results are summarized in the table on the nest slide..

If it were possible to measure the presence of copper in the hair of all males with epilepsy in the world, the average would be around 14 μg/g. This is an estimation, not an exact result.

The journal article that contains the results of the study actually reports that males with epilepsy have an average of 14±9 μg/g of copper in their scalp hair.

The  $\pm$ 9 is called the margin of error. This wording, however, does not mean that someone messed up the research. It simply means that no sampling method can guarantee that the sample exactly matches the population, but that the sampling techniques (when used correctly) can be trusted to give results that are accurate within a certain range.

So, 14±9 μg/g means:14 + 9 and 14 - 9.

14 + 9 = 23 and 14 - 9 = 5

Therefore the range is 5 μg/g to 23 μg/g.

Since the males with epilepsy in the sample showed an average of 14 μg/g of copper in their scalp hair, the researchers are fairly confident that the true average copper concentration for all males with epilepsy in the study is between 5 and 23 μg/g.

Example 1: Find Margin of Error

Find the interval of the true mean concentration of zinc for each group of subjects.

Base on the results, the true mean concentration of zinc show what connection about epilepsy?

Example 2: Margin of Error

1. What is the margin of error for the Fox News Poll?

2. What is the true percentage that voted No?

3. What is the true percentage that voted Yes?

4. What does mean?

Multiple Choice

Determine whether the survey clearly projects a winner. According to the survey of students voting for student council president, 42% of the students said they will vote for Jada and 58% said they would vote for Sean. The survey's margin of error is 5%

• Jada wins

• Sean wins

• It's too close to tell

• It's a tie

Multiple Choice

A recent survey found that 77% of high schoolers use their phones more than 4 hours a day on average. The margin of error was 3%. What is the interval for which we could expect to find the truth of the population?

• 77% - 80%

• 74% - 77%

• 74% - 80%

• 50 million high schoolers - 120 million

Multiple Choice

A recent survey found that out of 400 random American adults, 89% pay their bills on time. The margin of error in this survey was 2%. What is the interval of values in which the truth is likely found?

• 89% - 91%

• 87% - 89%

• 87% - 91%

• 388 - 402

Done!

Homework is Due on Friday.