Question

it is desired to estimate the mean GPA of each undergraduate class at a large university. how large a sample is necessary to estimate the GPA within 0.27 at the 90% confidence level? The population deviation is 1.2.

Answer 1

Standard Deviation ,σ = 1.2

sampling error        , E =0.27

Confidence Level   ,CL=90%

alpha     =1-CL           =10% or 0.10

Z value = Zα/2            = 1.645[excel formula   =normsinv(α/2)]

Sample Size,n = (Z * σ / E )² = (1.645*1.2/0.27) ²   =53.44

So,Sample Size needed=54