Motor Vehicle Use. The Federal Highway Administration...

Motor Vehicle Use. The Federal Highway Administration compiles information on motor vehicle use around the globe and publishes its findings in Highway Statistics. Following is a contingency table for the number of motor vehicles in use in North American countries, by country and type of vehicle, during one year. Frequencies are in thousands. a. How many cells are in this contingency table? b. How many vehicles are Canadian? c. How many vehicles are motorcycles? d. How many vehicles are Canadian motorcycles? e. How many vehicles are either Canadian or motorcycles? f. How many automobiles are Mexican? g. How many vehicles are not automobiles?

Motor Vehicle Use. The Federal Highway Administration compiles information on motor vehicle use around the globe and publishes its findings in Highway Statistics. Following is a contingency table for the number of motor vehicles in use in North American countries, by country and type of vehicle, during one year. Frequencies are in thousands.
a. How many cells are in this contingency table?
b. How many vehicles are Canadian?
c. How many vehicles are motorcycles?
d. How many vehicles are Canadian motorcycles?
e. How many vehicles are either Canadian or motorcycles?
f. How many automobiles are Mexican?
g. How many vehicles are not automobiles?

Key Concepts

Contingency Table

A contingency table is a type of table in a matrix format that displays the frequency distribution of variables. It allows the analysis of the relationship between two or more categorical variables by showing counts (or frequencies) organized according to their combinations in rows and columns.

Joint Frequency

Joint frequency refers to the count or frequency of cases that fall into two or more categories simultaneously as represented in the cells of the contingency table. Each cell in the table shows the number of observations that share a specific combination of the variables being analyzed.

Marginal Totals

Marginal totals are the sums of the frequencies for each row or column in a contingency table and are typically used to provide overall totals for each category of a single variable. They help in understanding the distribution of one variable irrespective of the other.

Inclusion-Exclusion Principle

The inclusion-exclusion principle is a counting technique used to correctly calculate the total number of elements in the union of different sets, ensuring that items counted in multiple sets are not counted more than once. It is especially useful when determining the number of observations that satisfy at least one of multiple criteria.

Transcript

00:01 All right, in this question, you're given a three by three contingency table.

00:08 And so when i'm referring to that three by three there, i'm describing the three choices of countries that you have and the three categories of or types, right, of vehicles that you have, all right, to choose from.

00:26 So that's the two variables that are being measured to get my bivari data.

00:32 The first question asks, how many cells in the contingencies table? sorry, so that's just your blue.

00:39 Okay, that's just what's inside the bold line in your table.

00:43 Okay, so just those nine cells, okay, not everything, not every square on the picture, just inside the dark, bolded lines.

00:52 And then it asks you how many below.

00:56 Belong to a certain country.

00:58 Okay, so this is asking for all of the cars observed for this country.

01:05 So you want the total.

01:06 So you go down to that marginal area there to get that total number.

01:11 And then remember, it's asking for how many actual vehicles.

01:15 And if you go back up to the paragraph before the picture, you'll see the question says that the frequencies are in thousands.

01:21 So you're going to take that number, which already looks like it, saying 20 ,000, but it represents thousands.

01:30 Okay? so that's actually representing 20 million cars belonging to that country.

01:37 Okay? so make sure to adjust the values of your numbers that way for each answer.

01:42 The third part asks how many are a certain type of vehicle.

01:48 So now you're looking at rows.

01:51 But again, you want all of that type.

01:54 So you're going to come down here to the margin and get the, that total for that type.

01:59 And again, remember to take the number and change it to thousands at three zeros at the end.

02:07 This really represents four million.

02:09 And then we've got, now here, this is intriguing.

02:13 And this part of the question they ask, they put together the name of the country and the name of a vehicle.

02:19 So by describing it as, so in this case, canadian motorcycles, they're saying, and i want to count both motorcycles and the fact that they're from canada.

02:35 Okay.

02:36 So now you're asking for a joint frequency.

02:40 All right.

02:40 So now you're looking in the blue cells where this row and column overlap.

02:46 Okay.

02:47 Now you're going to reach for there.

02:49 But it's still in thousands.

02:50 You're still going to add three zeros at the end to get like 300 ,000, not just 320.

02:56 Okay.

02:56 So like 320 ,000 canadian motorcycles...