Q 19. - The Practice of Statistics for AP

Question

Attitudes toward recycled products Recycling is supposed to save resources. Some people think recycled products are lower in quality than other products, a fact that makes recycling less practical. People who actually use a recycled product may have different opinions from those who don’t use it. Here are data on attitudes toward coffee filters made of recycled paper among people who do and don’t buy these filters:

(a) How many people does this table describe? How many of these were buyers of coffee filters made of recycled paper?

(b) Give the marginal distribution of opinion about the quality of recycled filters. What percent of consumers think the quality of the recycled product is the same or higher than the quality of other filters?  

Step-by-Step Solution

Answer

Part (a) The table lists $133$ people, $36$ of whom purchased coffee filters manufactured from recycled paper.

Part (b) As a result, $60.90$ percent of people believe the recycled product's quality is equal to or better than that of other filters.

Part (a) Step 1: Given Information

The table is 

	Think the quality of	the recycled product	is:
	Higher	The same	Lower
Buyers	20	7	9
Non buyers	29	25	43

Part (a) 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.

Part (a) Step 3: Calculation

The number of buyers and non-buyers are

$20 + 7 + 9 + 29 + 25 + 43 = 133$

The number of buyers is

$20 + 7 + 9 = 36$

As a result, the table lists $133$ people, $36$ of whom purchased coffee filters manufactured from recycled paper.

Part (b) Step 1: Concept

Marginal Distribution Percentage: $\frac{Row Total}{Table Total}\times 100$

Part (b) Step 2: Calculation

The table below shows the marginal distribution of opinions on the quality of recycled filters: Marginal Distribution Percentage: $\frac{Row Total}{Table Total}\times 100$

Table Total=$133$

Over $60.90$ percent ($36.8$ percent $+$ $24.1$ percent) of those polled believe the recycled product's quality is on par with or better than that of other filters.

As a result, $60.90$ percent of people believe the recycled product's quality is equal to or better than that of other filters. 

Marginal distribution table
Opinion	Buyer	Non buyers	Row total	Percent
Higher	20	29	49	49/133*100	36.8%
The same	7	25	32	32/133*100	24.1%
Lower	9	43	52	52/133*100	39.1%
Total	36	97	133