Q 21. - The Practice of Statistics for AP

Question

Attitudes toward recycled products Exercise $19$ gives data on the opinions of people who have and have not bought coffee filters made from recycled paper.

To see the relationship between opinion and experience with the product, find the conditional distributions of opinion (the response variable) for buyers and nonbuyers. What do you conclude?

Step-by-Step Solution

Answer

Filter paper is thought to be of great quality by $55.56$ percent of purchasers. And $44.3$ percent of non-buyers believe that filter paper is of poor quality.

Step 1: Given Information

The given data of who have and have not bought coffee filters made from recycled paper is: 

	Think the quality of	the recycled products	is:
	higher	The same	Lower
Buyer	20	7	9
Non buyer	29	25	43

Step 2: Concept

The distribution of a category variable is displayed using pie charts and bar graphs. Any set of quantities measured in the same units can be compared using bar graphs. It's a good idea to ask yourself, "What do I see?" when looking at any graph.

Step 3: Calculation

For non-buyers of coffee filters made of recycled paper, the conditional distribution of opinion (the response variable) is as follows: 

We can deduce from the above table of the conditional distribution of opinion (the response variable) for buyers and non-buyers of coffee filters made of recycled paper that the majority of people ($55.546$ percent) who buy coffee filters made of the recycled paper believe the filter paper is of high quality. Furthermore, $44.3$ percent of non-buyers of coffee filters made of the recycled paper believe that the quality of filter paper is poor. As a result, $55.56$ percent of purchasers believe filter paper is of great quality. And $44.3$ percent of non-buyers believe that filter paper is of poor quality. 

Conditional distribution table for non buyer of coffee filters of recycle paper
Opinion	Non buyer
	Total no.	Percentage
Higher	29	29/97*100	29.9
the same	25	25/97*100	25.8
lower	43	43/97*100	44.3
Total	97		100