Chapter 11: Q. 63 (page 759)

“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

Expert verified

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.