In a national survey of 500 business and 500 leisure...

In a national survey of 500 business and 500 leisure travelers, each was asked where he or she would most like "more space."a. Express the table as percentages of the total. b. Express the table as percentages of the row totals. Why might one prefer the table to be expressed this way? c. Express the table as percentages of the column totals. Why might one prefer the table to be expressed this way?

In a national survey of 500 business and 500 leisure travelers, each was asked where he or she would most like "more space."a. Express the table as percentages of the total.
b. Express the table as percentages of the row totals. Why might one prefer the table to be expressed this way?
c. Express the table as percentages of the column totals. Why might one prefer the table to be expressed this way?

Key Concepts

Contingency Tables

Contingency tables are used in statistics to display the frequency distribution of variables. They allow you to see joint occurrences across two categorical variables, facilitating the analysis of relationships and comparisons between different groups.

Overall (Grand) Percentages

Overall percentages, or percentages of the total, are calculated by taking the cell value, dividing it by the grand total from all cells, and then multiplying by 100. This method provides a global view of how the total counts are distributed across the different categories within the table.

Row Percentages (Conditional on Row Totals)

Row percentages are computed by dividing each cell value by its corresponding row total and then multiplying by 100. This approach highlights the distribution of responses within each group, making it easier to compare relative frequencies among different categories on a per-group basis.

Column Percentages (Conditional on Column Totals)

Column percentages are determined by dividing each cell value by its column total and multiplying by 100. This method is useful for understanding the composition of a particular outcome or category across different groups, offering insights into how the column variable distributes among the rows.

Transcript

00:01 Chapter 3 .1, question 3, gives us this chart right up here, where they interviewed 1 ,000 people, 500 business, and 500 leisure, and asked them where they would like more space, whether it would be in the plane, the hotel, or other.

00:16 So, question b, asks us to put these in percentages based on the row.

00:21 So that would be all the business in this case, or all the leisure.

00:25 Now, we know the totals for each of these are about 500 because it's given to us in the problem.

00:30 So we can go ahead and figure out the percentage is pretty easy by just dividing the number by the total.

00:35 So we go ahead and run through this.

00:38 We have 355 divided by 500 gives us 71%.

00:42 And then we have 95 divided by 500 is 19%.

00:46 50 over 500 is 10%.

00:49 Now we go down to the leisure.

00:51 We can do 250 divided by 500.

00:53 That's once again 50%.

00:55 Then we go to the next one, 165 divided by 500.

00:59 That is 33%, and then 85 divided by 500 is 17%.

01:08 Now, c, asks us to do the exact same thing, but in rows.

01:12 So rows are the up and down.

01:13 So in this case, all of the plane, all of the hotels, or all of the other.

01:17 That doesn't matter whether their business or leisure.

01:20 It's just how many people want a plane, how many people want a hotel, and how many people wanted other.

01:25 So going down here, the first thing we have to do is get the totals.

01:28 Part b was nice because we already had the totals for each row because it was given to us.

01:32 But in this we have to add it together.

01:34 So we add together 355 and 250, and that gives us a total of 605 that would want more space in the plane...

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