Exhibit 7-3
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study.
-Refer to Exhibit 7-3. The standard deviation of , known as the standard error of the proportion is approximately
A)0.5477
B)5.477
C)0.05477
D)54.77

Question

Exhibit 7-3
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study.
-Refer to Exhibit 7-3. The standard deviation of  , known as the standard error of the proportion is approximately
A)0.5477 
B)5.477 
C)0.05477 
D)54.77

Quizplus · Accepted Answer

The formula for the standard error of the proportion is:
standard error of the proportion = sqrt(p*q/n)

where:
p = proportion of success
q = proportion of failure (q = 1-p)
n = sample size

In this case, p = 0.4 (proportion of students living in dormitories), q = 0.6 (proportion of students not living in dormitories), and n = 80 (sample size).

Substituting the values, we get:
standard error of the proportion = sqrt(0.4*0.6/80) = 0.05477 (approx.)

Therefore, the standard deviation, known as the standard error of the proportion, is approximately 0.05477 or choice C.

Exhibit 7-3 in a Local University, 40% of the Students Live in Live