**The organizer of the seafood festival is hosting a clam chowder competition with the following conditions:**

**– There are twelve restaurants that are participating in this contest.**

**– As per the rules of the contest, each participant has to list all of its ingredients.**

**– The judge tastes the clam chowders and gives a rating on a scale of 1 to 10 on a notecard.**

**– Twenty-five note cards are selected by the organizer on a random basis.**

**– The organizer thinks that there is a relationship between the judge’s rating points given to each contestant and the number of ingredients used by the contest in making their respective clam chowders.**

**Which of the following statistical tests is the best option to determine above given relationship?**

**– Checking independence using the chi-square method**

**– Checking the difference of meansÂ using the 2-sample t-test**

**– Checking the proportion difference using the 2-sample z-test**

**– Checking the slope using the t-test of linear regression**

**– Checking the mean difference using the t-test of matched pairs**

The aim of this question is to understand the above-**given test****s** and identify which tests are **most suitable** for the given condition.

A **chi-squared test** is used to see if two clusters of data within a given population are **statistically related or independent**. A **2-sample t-test** is used for checking the **difference between the means** of two clusters in a population. A **2-sample z-test** uses the means of two clusters to see if they **belong to the same population or not**.Â A **1-sample t-test** is used for checking whether the **slope of the given data** after regression/fitting is zero or not. A **paired t-test** is used to see if the **mean difference between two clusters** is the same or not.

## Expert Answer

Based on the **situation given,** we can conclude that the **organizer wishes** to find whether the t**wo given parameters are related or not**. So based on the application areas described in the above paragraphs against each test type out of the given options, one can conclude that the **chi-squared test of independence** is the **most suitable statistical test** for this condition.

## Numerical Result

A **chi-squared test** should be used.

## Example

For the **same scenario given above**, let’s assume that the **chi-squared test is positive** and there exists a relationship between the ingredients of the clam chowders and the judge’s ratings. **How can the organizer model this relationship**?

To model the relationship between these two parameters, the organizer will have to perform a **regression analysis**. It can be a **linear regression** or a **multi-variable regression** depending on the **fitting accuracy**. However, he may have to perform some **additional tests** such as the **1-sample t-test** described above.