Question

Suppose a professor splits their class into two groups: students whose last names begin with A-K and students whose last names begin with L-Z. If p1 and p2 represent the proportion of students who have an iPhone by last name, would you be surprised if p1 did not exactly equal p2?

If we conclude that the first initial of a student's last name is NOT related to whether the person owns an iPhone, what assumption are we making about the relationship between these two variables?

Answer 1

(a)

Question asked:
Would you be surprised if p1 did not exactly equal to p2?
Answer : No

REASON: The number of students whose last name begins with A is not equal to the number of students whose last name begins with B. Similarly for all alphabets, the number will be different.

Thus:

we have two groups:

Group 1: students whose last names begin with A - K

Group 2: students whose last names begin with L-Z.

n1 = size of Group 1

n2 = size of Group 2

such that

n1 + n2 = N, size of the class.

By our above argument, we note:

n1 need not be equal to n2.

Thus,

p1 = n1/N need not be equal to p2 = n2/N

(b)

If we conclude that the first initial of a student's last name is NOT related to whether the person owns an iPhone:

The assumption we are making about the relationship between these two variables is as follows:
The two variables:

Variable 1: First initial of a student's last name

Variable 2: the person owns an iPhone

are belonging to two different populations and the two variables are independent.