Question

Students have an average GPA of 2.78 with a standard deviation of 0.45.

You have been tasked by the university president to select a random sample of students, and to conduct in-depth interviews with them about how their academics were impacted by COVID-19. We would like the random students that you select to be representative of the entire student body, and therefore the GPA of your sample should be within 0.2 grade points of the population mean.

How many students should you randomly select for interviews if you want to be 99% sure that the mean GPA of your interviewees is between 2.58 and 2.98?

Answer 1

Solution :

µ = 2.78
σ = 0.45

X : GPA of students

Margin of Error = E = 0.20

C = 99%,

For C = 99% , Zc = 2.57+2.58)/2 = 2.575 ( using normal table )

Sample size = ((Zc*σ)/E)^2 = ((2.575*0.45)/0.20)^2 = 33.57 ~ 34

Answer : Sample size required is 34