A college administrator would like to estimate the average grade point average (average of GPA) of all the current registered students based on a random sample. He plans to estimate the average GPA to within 0.05 with 90% confidence interval. At least how many students does he need to include in the sample in order to accomplish that? Assume the standard deviation of all GPA's in the student population is \sigma σ = 0.4.
Accepted Solution
A:
Answer: 346Step-by-step explanation:Given : Margin of error : E= 0.05Standard deviation : [tex]\sigma=0.4[/tex]Significance level :[tex]\alpha=1-0.9=0.1[/tex]Critical value : [tex]z_{\alpha/2}=1.645[/tex]The formula to calculate sample size ( if proportion is known) :-[tex]n=(\dfrac{z_{\alpha/2}\sigma}{E})^2\\\\\Rightarrow\ n=(\dfrac{(2.326\times0.4)}{0.05})^2\\\\\Rightarrow\ n=346.257664\approx346[/tex]Hence, the required minimum sample would be 346.