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## AP®︎/College Statistics

### Unit 1: Lesson 4

Statistics for two categorical variables

# Conditional distributions and relationships

AP.STATS:
UNC‑1 (EU)
,
UNC‑1.R (LO)
,
UNC‑1.R.1 (EK)
CCSS.Math:

A small private college was curious about what levels of students were getting straight A grades. College officials collected data on the straight A status from the most recent semester for all of their undergraduate and graduate students. The data is shown in the two-way table below:
Straight A's24060300
Not3, comma, 7604404, comma, 200
Total4, comma, 0005004, comma, 500
Problem 1
A distribution in the data is highlighted below.
What type of distribution is this?
Straight A's24060300
Not3, comma, 7604404, comma, 200
Totalstart color #1fab54, 4, comma, 000, end color #1fab54start color #1fab54, 500, end color #1fab54start color #1fab54, 4, comma, 500, end color #1fab54

problem 2
What conclusion can we draw from the highlighted distribution?

problem 3
Officials at the college are curious if one level of student was more likely to get straight A's than the other.
Calculate the conditional distribution of straight A status for each level of student.
Straight A's24060300
Not3, comma, 7604404, comma, 200
Total4, comma, 0005004, comma, 500
Straight A's
percent
percent
Not
percent
percent

problem 4
Based on these conditional distributions, what can we say about the association between student level and straight A status?

Problem 5
For this college, is there an association between the level of student and whether or not the student has straight A's?

## Want to join the conversation?

• In the answer options of the problem 4, what is the difference between the option B and C? I think both answers are correct. Are not they?
(1 vote)
• Choice C is like this :
C: Straight A students ( Total is 300 students ) were more likely to be graduate ( 60 students) than undergraduate ( 240 students) !
in other words; if all students who got Straight A (graduate + undergraduate) gathered in one class, then most of them would be graduate or undergraduate?
(1 vote)
• The wording is SO confusing to me.
You wrote in Problem 3:
"Calculate the conditional distribution of straight A status for each level of student."
How do I know if I should focus on the OF (straight A) or the FOR (each level of student)? Do I calculate row or column?
Either I am stupid in English or it is really confusing.
• We're finding the conditional probability of x (the numerator) for each of y (clue that it should go in the denominator).

If they asked "Find the conditional probability of level of study for straight A status" then these would be reversed.
• The explanation of the first example states that "A conditional distribution turns each count in the table into a percentage of individuals who fit a specific value of one of the variables.", but in the exercise the values aren't always percentages; just counts! Is the article definition incorrect?
• From the author:That definition is correct! The first conditional distribution in this article appears in Problem 3.
• Question 5: Is a 6 procent difference enough to conclude that there is a correlation between the two variables?
• It depends on alpha level set by the researcher. If it is .05 it won't pass. If it is .1 it will pass.
• I believe that Problem 2 is ambiguous, as it asks for one correct answer which is C, but both B and C appear to be correct answers. B says "There are far more students without straight A's than there are with straight A's.", which seems to be true, given a ratio of 4200 to 300.
• From the author:Problem 2 asks what conclusion we can draw from the highlighted distribution, and the highlighted distribution only tells us about the ratio of undergraduate to graduate students.
• Example problems are helpful and all, but how come there aren't any written definitions for what Marginal and Conditional Distribution are?
(1 vote)
• There is, watch the video carefully and read the explaination
(1 vote)
• I have a quick question about Problem 4.

It says the third choice is wrong because "Note: The third choice is wrong because there are 300
total students with straight A's, and a majority of them
240/360≈67% were undergraduate students. This doesn't mean that undergraduate students are more likely to have straight A's though. There were a lot more undergraduate students than graduate students in general, so a lot of the straight A's students are undergraduates. However, a low percentage of undergraduate students had straight A's."

I think that should be 240/300 = 80% rather than 240/360 = 67%.
• A typo? 240/360≈67%. should be 240/300 = 80%