P 1 and P 2 are expected as the same 2 groups with students in the 2 groups being as follows:
Group 1: students whose last names begin with A-K
Group 2: students whose last names begin with L-Z
N 1 = size of group 1
N 2 = size of group 2
Meaning; N 1 + N 2 = the size of the class
From above
N 1 = size of group 1
N 2 = size of group 2
Meaning; N 1 + N 2 = the size of the class
We expect the proportion of the class is
N 1 = 12, (A-K) iPhone ownership=1
The proportion is 1/12= 0.08
Similarly, for group 2 (L-Z)
N 2 =1/16 (L-Z) and iPhone ownership is 1
Therefore, the proportion is 1/16 which is 0.06
The total proportion is therefore 0.06+0.08=0.14
As such, this is different from the population proportion of 0.66
It is not surprising the P 1 and P 2 are not the same. This is because there is a difference between the number of students whose last name starts with A and those whose names start with B. In other words, all alphabets numbers will be different.
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N 1 + N 2 = the size of the class meaning there is no need of N 1 and N 2 to be equal
Therefore, P 1 = N 1 /N which does not have to be equal to P 2 = N 2 /N
If one concluded that the last name of the person does not correspond to them owning an iPhone, the assumption being made between the two variables, therefore, is
Variable 1= is first initial of student’s last name
Variable 2=the person owns an iPhone
This means that they are belong to different populations and the two variables are therefore, independent
