Question

Assume that all​ grade-point averages are to be standardized on a scale between 0 and 4. How many​ grade-point averages must be obtained so that the sample mean is within 0.013 of the population​ mean? Assume that a 95​% confidence level is desired. If using the range rule of​ thumb, sigma can be estimated as StartFraction range Over 4 EndFraction equalsStartFraction 4 minus 0 Over 4 EndFraction equals1. Does the sample size seem​ practical? The required sample size is nothing. ​(Round up to the nearest whole number as​ needed.)

Answer 1

Sample size estimation for population standard deviation                  
                  
We have given here,                  
                  
Population standard deviation =1  
Margin of error =E=0.013  
Level of significance =   1-0.95=0.05  
Z critical value is (by using Z table) is = 1.96

Sample size formula is

  

  
= 22730.53

Therefore, sample size approximately will be 22731