Question

“Will changing the rating scale on a survey affect how people answer the question?” To find out, the group took an SRS of $50$students from an alphabetical roster of the school’s just over $1000$students. The first $22$students chosen were asked to rate the cafeteria food on a scale of $1$(terrible) to $5$(excellent). The remaining $28$students were asked to rate the cafeteria food on a scale of $0$(terrible) to $4$(excellent). Here are the data:

a. Was this an observational study or an experiment? Justify your answer.

b. Explain why it would not be appropriate to perform a chi-square test in this setting.

Short answer

Part a. This is an experimental study.

Part b. The condition of large counts is not satisfied so, could not use Chi-square test.

Step-by-step solution

Part a. Step 1. Explanation

First need to understand about the experimental study and observational study:

Experimental study: Assigning people or things to groups and applying some treatment to one group, while the other group does not receive the treatment.

Observation study: In an observational study, measure or survey members of a sample without trying to affect them.

The study having two groups in which they are asking for a rating. Therefore, it is experimental study.

Part b. Step 1. Given information

Given:

Part b. Step 2. Explanation

The expected values are:

The expected values of some categories less than $5$. Therefore, the condition of large counts is not satisfied. Hence, could not use Chi-square test.