Attitudes toward recycled products Recycling is supposed to...

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:16 (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?

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:16
(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?

Key Concepts

Contingency Table

A contingency table is a statistical tool used to display and analyze the relationship between two or more categorical variables by organizing data into rows and columns. This format makes it straightforward to see the distribution of subjects across different categories and to calculate totals, which are useful for further analysis.

Marginal Distribution

Marginal distribution refers to the totals calculated for each row or column in a contingency table, representing the overall frequency of each category irrespective of the other variable. It provides a summary view of one dimension of the data, allowing easy comparison between different groups or categories.

Percentage Calculation

Percentage calculation involves converting raw counts into percentages to facilitate comparison between groups, especially when the groups have different sizes. This method is crucial in interpreting survey or observational data because it provides a normalized view of the distribution of responses, making trends easier to identify.

Survey Data Analysis

Survey data analysis involves summarizing and interpreting responses obtained from questionnaires to understand opinions, behaviors, or characteristics of a population. It includes organizing data into formats like contingency tables, calculating distributions, and drawing inferences about the attitudes or trends present in the surveyed responses.

Transcript

00:01 Question 19, we're given a two -way table that includes data on the opinions of consumers on whether recycled coffee filters are of better, same, or lower quality than non -recycled filters.

00:15 So for any two -way table, it means that we have two variables that are represented.

00:21 So one variable in this case is the opinion of the consumers, and that's split into three categories.

00:27 So some think the recycled filters are of higher quality.

00:31 Some think they're the same.

00:33 Some think they are lower.

00:36 And the other variable, the second variable, is that of the consumer type.

00:42 So we have buyers and we have non -buyers.

00:52 So if we look at the data that's provided in the question, we have 20 buyers who think that recycled filters are of better quality.

01:01 Seven to think they're the same.

01:03 Nine you think they're lower.

01:04 And then for non -buyers, we have this information.

01:14 So part a asks, what are the total number, what is the total number of people that the table represents? now the quick answer is you can just sum these six cells that we see here because there is no overlap in any of these cells.

01:29 So if you sum these, you'll get to your answer.

01:31 And these actually summed to 133.

01:34 But just to take this in a slightly more formal direction, any time you're asked to extract information from a two -way table, a good starting point is to add up all the rows and add up all the columns.

01:45 So if we add up the rows, we have 36 here, 78, and here we have 97, i believe.

01:59 Adding up the columns, 49, 32, and 52.

02:11 So we can add up all of the six original cells, or we can add up the rightmost column, or add up the bottom -most row.

02:20 They all come out to 133.

02:25 So the answer to the first part of a is, there are 100 ,000.

02:30 33 people represented by the table...

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