# Do Placebos Kill Minotaurs?

## Formulating Statistical Hypotheses and Hypothesis Testing

William Thompson, Diana Gedye, David Thomas | Published: June 11th, 2024 by K20 Center

• Subject
• Course AP Statistics
• Time Frame 3-4 class period(s)
• Duration 180 minutes

### Summary

In this lesson, students will explore the concepts of statistical hypotheses by looking at what a statistical hypothesis is, how they are formed, and some methods of testing them. Once they have been introduced to the basic concepts, they will be able to apply these concepts by playing Potions!, a digital game-based learning (DGBL) module, followed by a chance to extend what they've learned by applying the concepts to a real-world question. This lesson includes optional modifications for distance learning. Resources for use in Google Classroom are included.

### Essential Question(s)

How do we formulate hypotheses, and more importantly, how do we test them once we have them?

### Snapshot

Engage

Use the Examples and Non-examples Strategy to gauge the current understanding of students about what a hypothesis is and how you determine if an experiment supports a hypothesis or not.

Explore

Students play the first two levels of the Potions! DGBL module as a further introduction and chance to apply the concepts they've learned so far.

Explain

Students use the DOK Question Stems learning strategy to develop deeper thinking about the concepts they've learned and compare their understanding of those concepts.

Extend

Students extend their understanding of the concepts by playing the third and fourth studies in the Potions! DGBL module.

Evaluate

Students evaluate understanding using the Strategy Harvest learning strategy.

### Instructional Formats

The term "Multimodality" refers to the ability of a lesson to be offered in more than one modality (i.e. face-to-face, online, blended). This lesson has been designed to be offered in multiple formats, while still meeting the same standards and learning objectives. Though fundamentally the same lesson, you will notice that the different modalities may require the lesson to be approached differently. Select the modality that you are interested in to be taken to the section of the course designed for that form of instruction.

### Materials

• Computers with Internet access or an iPad for each student

• K20 Game Portal accounts or iPad apps of Potions! for each student

• Whiteboard

• Writing materials (pen, pencil, paper, etc.)

• DOK Question Stems (attached)

• Strategy Harvest Worksheet (attached)

• Fun Size package of M&M's (one for each student)

### Engage

Use the Examples and Non-Examples strategy to gauge your students' current understanding of the concepts. On a whiteboard, or a similar space, write Hypothesis, and then, have your students write what they think that term means on sheets of paper. Then, give one example of what the term is and one of what the term is not.

Once students have finished writing, discuss the term and the examples students came up with as a class.

Write the term Hypothesis Testing on the board and complete the exercise again.

Below are definitions for some other important terms you may wish to emphasize during this exercise:

• Hypothesis—an assumption made about a population parameter that may or may not be true

• Hypothesis Testing—the formal methods and procedures used to determine if a hypothesis should be accepted or rejected

• Sample—a set of collected data

• Population—the entire pool from which a sample is drawn

### Explore

Help students set up their computers or tablets to play the game and then have them play through the first two studies, which should take roughly 30-45 minutes. You do not need to give them further instructions here. The game will introduce them to its mechanics, concepts, and story. At this point, take time to walk around the room, helping students who are confused or stuck, and observing their progress. The instructor's guide (located under Attachments) provides information on the game's interface to help you.

### Explain

Once your students have all finished the first few studies of Potions!, you can start going a bit deeper in explaining the concepts. Use the DOK Question Stems strategy to help your students formulate some questions related to what they've learned so far. Pass out copies of the attached DOK Question Stems worksheet to each student and have them come up with 1–2 questions from levels 1, 2, and 3. Then, pair your students up and have them quiz each other on the questions they've asked.

Have them note any questions they were not able to answer. Then, have pairs join together into four-person groups and quiz each other again, again noting any questions their group was not able to find an answer to. While this is going on, walk around the room and correct any wrong answers or misconceptions you hear.

After all the groups have finished, discuss any questions they could not answer and see if any other groups can offer answers to those questions, answering and explaining the concepts, yourself, if none of the other students can. Again, make sure to correct any misconceptions your students may have about the concepts.

### Extend

Now, give your students a chance to spend more time applying what they have learned. Have them play through the third and fourth studies of the Potions! DGBL module. This should take them another 30 to 45 minutes to complete. If you have any students who complete the game significantly faster than their peers, you can have them attempt the fifth study as well, but keep in mind, that this study is designed to be significantly more challenging.

As before, you should spend this time walking around the room and helping students who may be having trouble. The same tips mentioned in the Explore section will be helpful here as well. Make sure they are focusing on the means and comparing them, that they are using sufficient sample sizes, and that placebos do not use up their resources. Remind them that they cannot save every creature. So, if one creature is proving too difficult to save, they can always switch to a different one.

### Evaluate

To evaluate your students' understanding of the concepts, use the Strategy Harvest strategy. Give each student a package of M&M's and a Strategy Harvest Worksheet (located under Attachments). Have them develop a hypothesis about the package of M&M's and then think about how they would test that hypothesis, other than just counting how many M&M's are in the bag.

If your students are having trouble coming up with hypotheses, here are some examples:

• Fun Size M&M's are 20% orange.

• The average number of M&M's in a Fun Size package equals 18.

• A Fun Size bag of M&M's will have an equal distribution of colors.

Once students have each written down their strategy and hypothesis, have them find a partner to compare with, taking notes on each other's strategies and hypotheses. Then, have them repeat this process with a second student, again making sure to take notes.

Once students have compared strategies with two other students, have them return to their seats and put their original strategy into practice to determine whether their hypothesis is supported by the results. Have students share their results with the class and discuss them.