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# Activity: Chocolate tasting experiment

## Achievement objectives

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• S 7-4 Investigate situations that involve elements of chance:
• A – comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions
• B – calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology.

## Indicators

• Uses two-way frequency tables to solve simple probability problems, including starting to work with simple conditional probabilities.
• Learns that situations involving real data from statistical investigations can be investigated from a probabilistic perspective.

## Specific learning outcomes

Students will be able to:

• understand and use two-way tables.

## Diagnostic snapshot(s)

As an introduction, collect some data from the class and record it in a two-way table, for example, whether students have or have not been to both the North and South Islands of New Zealand. (Alternative categories would be needed for single sex classes.)

 Boys Girls Been to both North and South Islands Not been to both the North and South Islands

Guide the students on generating probability questions, including conditional probability, using this data. For example:

• What is the probability that a student in our class has been to both the North and South Islands?
• What is the probability that a girl/boy in our class has been to both the North and South Islands?
• What is the probability that a student in our class, who has been to both the North and South Islands, is a girl or a boy?

## Planned learning experiences

### Setting the scene

Select two brands of a single product, for example, chocolate.

The scenario involves students stating their prior preference for one of the brands over the other, doing a blind taste test of the same two brands, and then stating a preference for one of the samples tasted.

Before starting, describe the activity and get students to brainstorm possible questions they could ask of the data.

Look at the questions asked by the class during this initial set up. Talk them through the need for presenting the data in a way that enables them to answer questions such as:

• Are students who select brand A as their preferred brand more likely to prefer brand A or brand B in a blind taste test?
• What is the probability that a student in our class who liked brand B in a blind taste test also had this as their preferred brand?
• What is the probability that a student in our class selects brand B as their preferred brand and also prefers brand B in a blind taste test.

(“Brand A” and “brand B” can be replaced with the actual brand names in the classroom.)

### Collecting the data

• Students record their preferred brand in their books before any blind tasting begins.
• Students then taste test the two brands blindfolded and state which sample they prefer.
• Randomise the order of tasting, that is, some will taste brand A and first, and some will taste brand B.

#### White choc. Which brand of chocolate do you prefer?

 My original preference Blind taste preference .... ....

Overall class response to the question: Which brand of chocolate did you prefer before blind tasting?

Prefer brand A _____________ Prefer brand B ____________

Overall class response to the question: Which brand of chocolate did you prefer in the blind tasting test?

Prefer brand A _____________ Prefer brand B ____________

The students then develop a two-way table showing the original preference and the preference in the blind tasting.

#### Class results

 Brand A stated as original preference Brand B stated as original preference TOTALS Brand A chosen in the blind tasting Brand B chosen in the blind tasting TOTALS

Use the two-way table to answer the questions posed by the class in the initial set up.

Last updated September 17, 2018