Question

Suppose that the average grade on our midterm exam (in our class of size 116 students) was 75. Which is more likely to be closer to 75:

a) the exam grade of a randomly selected student in the class?

b) the mean exam grade of a randomly selected sample of 10 students in the class?

Explain your reasoning.

Answer 1

Correct answer is

b) the mean exam grade of a randomly selected sample of 10 students in the class

Reason:

case a) When we consider the entire class,

the standard error = standard deviation

Case b) When we consider randomly selected sample of 10 students in the class then

the standard error = standard deviation/ sqrt(sample size)

Thus, Standard error in case b) < Standard error in case a)

Now, if the standard error is small then the value is closer to mean value (as x = mean +- z*standard error)

Thus. case b) the mean exam grade of a randomly selected sample of 10 students in the class is more likely to be closer to 75